`sum_(n=1)^oo 5^n/n^4` Use the Root Test to determine the convergence or divergence of the series.

To determine the convergence or divergence of a series `sum a_n` using Root test, we evaluate a limit as:

`lim_(n-gtoo) root(n)(|a_n|)= L`

or

`lim_(n-gtoo) |a_n|^(1/n)= L`

Then, we follow the conditions:

a) `Llt1` then the series is absolutely convergent.

b) `Lgt1` then the series is divergent.

c) `L=1` or does not exist  then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.

We may apply Root...

To determine the convergence or divergence of a series `sum a_n` using Root test, we evaluate a limit as:

`lim_(n-gtoo) root(n)(|a_n|)= L`

or

`lim_(n-gtoo) |a_n|^(1/n)= L`

Then, we follow the conditions:

a) `Llt1` then the series is absolutely convergent.

b) `Lgt1` then the series is divergent.

c) `L=1` or does not exist  then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.

We may apply Root test on the given series `sum_(n=1)^oo 5^n/n^4` when we let:  `a_n =5^n/n^4` .

Applying the Root test, we set-up the limit as: 

`lim_(n-gtoo) |5^n/n^4|^(1/n) =lim_(n-gtoo) (5^n/n^4)^(1/n)`

Apply Law of Exponent: `(x/y)^n = x^n/y^n` and `(x^n)^m= x^(n*m)` .

`lim_(n-gtoo) (5^n/n^4)^(1/n) =lim_(n-gtoo) (5^n)^(1/n)/(n^4)^(1/n)`

                       ` =lim_(n-gtoo)5^(n*1/n)/n^(4*1/n)`

                       ` =lim_(n-gtoo)5^(n/n)/n^(4/n)`

                       ` =lim_(n-gtoo)5^1/n^(4/n)`

                       ` =lim_(n-gtoo)5/n^(4/n)`

Evaluate the limit.

`lim_(n-gtoo) 5/n^(4/n)=5 lim_(n-gtoo) 1/n^(4/n) `         

                ` =5 *1/oo^(4/oo)`

                ` =5 *1/oo^(0)`

                ` =5 *1/1`

                ` = 5*1`

                ` =5`

The limit value `L =5` satisfies the condition: `Lgt1` since `5gt1` .

Conclusion: The series `sum_(n=1)^oo 5^n/n^4` is divergent.

A Modest Proposal Irony

Dramatic irony occurs when the audience or reader knows more than the character. Some might find it difficult to argue for the existence of dramatic irony in this essay, but if you were going to make a case for it, you could argue that the reader is certainly supposed to realize that the speaker presents an incredibly awful idea—despite the fact that the speaker thinks it is fantastic. 

Other kinds of irony are easier to...

Dramatic irony occurs when the audience or reader knows more than the character. Some might find it difficult to argue for the existence of dramatic irony in this essay, but if you were going to make a case for it, you could argue that the reader is certainly supposed to realize that the speaker presents an incredibly awful idea—despite the fact that the speaker thinks it is fantastic. 

Other kinds of irony are easier to find. Irony, generally speaking, occurs when there is some discrepancy between expectation and reality.  For example, when we read the title of this text—"A Modest Proposal"—we might expect, perhaps, a humble speaker presenting an uncontroversial idea: something suitably "modest."  The reality is that this speaker is hardly humble—he thinks highly of himself and his idea for ridding the country of beggars—and the idea he presents could hardly be more controversial!  He proposes that one-year-old children be sold as a source of food, so it would be difficult to imagine a proposal less modest than this one. 

Another example of irony is that the speaker believes that his solution would solve many problems for the country, not the least of which is "that it will prevent those voluntary abortions, and that horrid practice of women murdering their bastard children, alas! too frequent among us."  He laments how common it is for women to kill their children, but his plan is tantamount to the same thing!  What is the difference between someone killing their child to preserve their reputation or selling their child to be someone's dinner?  After such a statement as the above, we would expect the speaker's plan to somehow preserve or help these children.  In reality, he just wants women to keep their children alive long enough so they can net the women a profit.

`int 8^(-x) dx` Find the indefinite integral

By definition, if the function  F(x) is the antiderivative of f(x) then we follow

the indefinite integral as `int f(x) dx = F(x)+C`

 where: f(x) as the integrand

           F(x) as the anti-derivative function 

           C  as the arbitrary constant known as constant of integration

 For the problem` int 8^(-x) dx,` we may apply u-substitution then basic formula for exponential function.

Using u-substitution, we let `u =...

By definition, if the function  F(x) is the antiderivative of f(x) then we follow

the indefinite integral as `int f(x) dx = F(x)+C`

 where: f(x) as the integrand

           F(x) as the anti-derivative function 

           C  as the arbitrary constant known as constant of integration

 For the problem` int 8^(-x) dx,` we may apply u-substitution then basic formula for exponential function.

Using u-substitution, we let `u = -x`  then` du = -1 dx` .

By dividing both sides by -1 in `du = -1 dx` , we get `-1 du = dx` .

Applying u-substitution using` -x =u ` and dx=-1 du in ` int 8^(-x) dx`

, we get:  `int 8^(u) * (-1) du =  -1 int 8^u du`

Applying the basic integration formula for exponential function: 

`int a^u du = a^u/(ln(a)) +C` where a is a constant.

  Then `(-1) int 8^u du = 8^u/(ln(8)) +C`

To express  it in terms of x, we plug-in u=-x to get:

`-8^(-x)/(ln(8)) +C`

Recall `8 = 2^3` . It can be also be written as:

`-(2^3)^(-x)/(ln(2^3))+C`

Recall the logarithm property:` ln(x^n) = n ln(x)` then` ln(2^3) = 3 ln(2)`

It becomes 

 The final answer can be `-8^(-x)/(ln(8))+c ` or  `-2^(-3x)/(3ln(2))+C` .

How is imagery used in the story "The Notorious Jumping Frog of Calaveras County"?

Imagery refers to any description that appeals to our five senses: sight, sound, smell, taste, or touch. Imagery helps us to feel better connected to what we are reading, allowing us to imagine exactly what it is like to be in that moment.

Mark Twain uses large amounts of imagery in his short story "The Notorious Jumping Frog of Calaveras County." For instance, in the first couple of paragraphs he describes Simon Wheeler:

I found...

Imagery refers to any description that appeals to our five senses: sight, sound, smell, taste, or touch. Imagery helps us to feel better connected to what we are reading, allowing us to imagine exactly what it is like to be in that moment.

Mark Twain uses large amounts of imagery in his short story "The Notorious Jumping Frog of Calaveras County." For instance, in the first couple of paragraphs he describes Simon Wheeler:

I found Simon Wheeler dozing comfortably by the bar-room stove of the old, dilapidated tavern in the ancient mining camp of Angel's, and I noticed that he was fat and bald-headed, and had an expression of winning gentleness and simplicity upon his tranquil countenance. . . . Simon Wheeler backed me into a corner and blockaded me there with his chair, and then sat me down and reeled off the monotonous narrative which follows this paragraph. He never smiled, he never frowned, he never changed his voice from the gentle-flowing key to which he tuned the initial sentence, he never betrayed the slightest suspicion of enthusiasm

Here, we have lots of visual imagery, as Twain describes Wheeler "dozing comfortably" in a "dilapidated tavern." He also carefully describes Wheeler's physical appearance, saying he was "fat and bald-headed" with a "tranquil countenance." Finally, Twain describes how Wheeler behaved: he "backed me into a corner and blockaded me there with his chair" to tell his story. All of these descriptions give a vivid picture to the reader of what happened in the tavern.

Another example of imagery in the text is seen in Wheeler's storytelling. He says:

So he set there a good while thinking and thinking to hisself, and then he got the frog out and prized his mouth open and took a tea- spoon and filled him full of quail shot filled him pretty near up to his chin and set him on the floor. Smiley he went to the swamp and slopped around in the mud for a long time, and finally he ketched a frog, and fetched him in, and give him to this feller, and says . . . "Now, if you're ready, set him alongside of Dan'l, with his fore- paws just even with Dan'l, and I'll give the word."

Wheeler describes how the man "prized his mouth open" and "filled him full of quail shot pretty near up to his chin." This emphasizes the roughness that the man used with the frog and the amount of weight he added to it. We also see imagery as he describes how he "slopped around in the mud for a long time," which explains the messy process of frog hunting. Mark Twain draws readers into his tale by using a wide variety of descriptive imagery to help readers understand just how bizarre Wheeler's story (that he insists upon sharing with the narrator) really is.

What is the difference between globalization and cultural diffusion?

Globalismrefers to the integration of companies, resources, or markets from different areas of the world. With the innovations in communication and transportation that were realized in the last century, companies in one country can utilize other countries around the world in the execution of their operations. A company can have offices in the United States, manufacturing plants in Asia, customer service centers in Europe, and stores throughout the world. Globalism is a word used...

Globalism refers to the integration of companies, resources, or markets from different areas of the world. With the innovations in communication and transportation that were realized in the last century, companies in one country can utilize other countries around the world in the execution of their operations. A company can have offices in the United States, manufacturing plants in Asia, customer service centers in Europe, and stores throughout the world. Globalism is a word used to define this economic synthesis.  

Diffusion is a very similar word but is used to define the cultural sharing that occurs when groups from different areas of the world are joined. Cultural diffusion commonly occurs as a result of globalism. An example of cultural diffusion is how rap music originated in the United States, but can now be found in all parts of the world. Rap music is now recorded in dozens of different languages in all parts of the world.

What is the external conflict in "The Sniper"?

The main external conflict in "The Sniper" is the sniper's battle to stay alive.  This conflict involves multiple parts.  The conflict begins when the sniper lights his cigarette and gives his position away to the Free Stater sniper.  From this moment forward, the Republican sniper is in a battle for his life.  The enemy knows his location, and he must eliminate everybody that knows his location.  An old woman on the street flags down a...

The main external conflict in "The Sniper" is the sniper's battle to stay alive.  This conflict involves multiple parts.  The conflict begins when the sniper lights his cigarette and gives his position away to the Free Stater sniper.  From this moment forward, the Republican sniper is in a battle for his life.  The enemy knows his location, and he must eliminate everybody that knows his location.  An old woman on the street flags down a soldier in an armored vehicle, and she points up to the sniper's location.  If the sniper doesn't kill those two on the street, then reinforcements can be called to his location.  Under fire from the other sniper, the protagonist successfully kills the old woman and the soldier.  The sniper then uses some trickery to kill the enemy sniper.  

Another external conflict that exists in the story is the war itself.  It is a civil war between the Irish Republicans and the Irish Free Staters.  

What does Ivan do the first time he enters the exhibit?

Do you mean the mall exhibit or the zoo exhibit?

When Ivan first sees the cage at the mall, he is relieved. He had been living with Mack at Mack's house since he was a baby. But as he grew, he found it hard to maneuver around Mack's place without disruption. Ivan says,

"When I saw my new domain, I was thrilled, and who wouldn't have been? It had no furniture to break. No glasses to smash. No toilets to drop Mack's keys into."

Ivan also says,

"I was relieved to have my own place."

He notes, in particular, that his "new domain" has its own tire swing.

So, to Ivan, his cage at the mall is, at first, an improvement over his previous circumstances living with Mack. Ivan referred to that time as his "life as a human." Being at the zoo allows him to be more like a gorilla -- but not entirely.

Later in the book, when Ivan is taken to the zoo by Maya, he spends some time alone in a cage, isolated from the main gorilla exhibit by a glass door. He watches the other gorillas, and they in turn observe him. He learns the name of one of the gorillas. She is Kinyani.

When Maya opens the glass door, Ivan first spends time absorbing all the new sensory impressions the outdoor exhibit provides him:

"Sky.

Grass.

Tree.

Ant. 

Stick.

Bird. 

Dirt.

Cloud. 

Wind.

Flower.

Rock. 

Rain."

Soon after, he makes his first contact with the other gorilla residents. It does not go well. Kinyani chases him and throws a stick. He cowers and returns to his cage. He cannot remember how to properly interact with other gorillas at first, especially as a full-grown silverback male. His long-term social isolation at the mall has taken its toll.

Ivan soon tries again, however, and the next day intimidates a juvenile male who is eyeing his food and then builds a nest for himself. This is his first step toward assimilating into the gorilla group.

A hydrocarbon contains 14.2% hydrogen by mass. This compound has a relative molecular mass of 56g/mol. Calculate the empirical formula and the...

The empirical formula of a compound gives the simplest whole number ratio of atoms and the molecular formula gives the actual number of atoms of each element in a molecule. The molecular formula is a whole-number multiple of the empirical formula.

To find the empirical formula one must calculate the number of moles of each element in the compound. We are told that this is a hydrocarbon, meaning it contains hydrogen and carbon, and that...

The empirical formula of a compound gives the simplest whole number ratio of atoms and the molecular formula gives the actual number of atoms of each element in a molecule. The molecular formula is a whole-number multiple of the empirical formula.

To find the empirical formula one must calculate the number of moles of each element in the compound. We are told that this is a hydrocarbon, meaning it contains hydrogen and carbon, and that it is 14.2% hydrogen by mass. Therefore if we have 100 grams of this compound 14.2 grams will be hydrogen and the remaining 85.8 grams will be carbon.

Using the molar masses of hydrogen and carbon, convert both to moles:

14.2 g H x (1 mol/1.00g) = 14.2 moles H

85.8 g C x (1 mol/12.0 g) = 7.1 moles C

Now divide each number of moles by the smallest (7.1) to get a whole-number mole ratio:

(14.2 moles H)/(7.1) = 2

(7.1 moles C)/(7.1) = 1

The mole ratio of C to H is 2:1, so the empirical formula is `CH_2.`

To find the molecular formula, compare the given molar mass of the compound to the molar mass of the empirical formula:

Molar mass of compound = 56 g/mol

Molar mass of `CH_2` = (12.0) + 2(1.00) = 14.0 g/mol

56/14.0 = 4, so the molecular formula is 4 times the empirical formula:

`4(CH_2)` = `C_4H_8`

What is it about Montresor that makes him an especially effective enemy to Fortunato?

Montresor is an especially effective enemy of Fortunato for a few reasons, not the least of which are his intense pride and ability to manipulate. As he says early on, "I must not only punish but punish with impunity." He feels the need not only to avenge the wrongs done and insults given to him by Fortunato, but also to exact his revenge without having to endure some punishment for it. His family motto translates...

Montresor is an especially effective enemy of Fortunato for a few reasons, not the least of which are his intense pride and ability to manipulate. As he says early on, "I must not only punish but punish with impunity." He feels the need not only to avenge the wrongs done and insults given to him by Fortunato, but also to exact his revenge without having to endure some punishment for it. His family motto translates to "You will not harm me with impunity"—in other words, no one can harm a Montresor and get away with it. His personal and familial pride make him especially relentless and ruthless when it comes to Fortunato.

Further, Montresor clearly put a great deal of thought into his revenge, and he manipulates his staff and the public, as well as Fortunato, to achieve it. He tells his servants he will be gone all night and that they must remain at home, knowing they will all go to the festival as soon as he leaves (and will claim they were home all night to avoid trouble). He makes sure his costume covers his face so he will not be seen with Fortunato in public, and he concocts an elaborate story about a pipe of Amontillado, knowing Fortunato's pride will compel him to risk his own health in order to prove Montresor has been had. He is so thoughtful and manipulative, which makes him a perfect enemy for the relatively simple and straightforward Fortunato.

Which state is farthest east?

I am going to assume that you mean which state in the United States has the easternmost point.  Interestingly, the state that is the furthest east is also the state that is the furthest west.  The state that I am talking about is Alaska.  The reason that it is the farthest eastis because some of the Aleutian Islands cross the 180 degree line of longitude.  This places those islands in the eastern hemisphere; therefore,...

I am going to assume that you mean which state in the United States has the easternmost point.  Interestingly, the state that is the furthest east is also the state that is the furthest west.  The state that I am talking about is Alaska.  The reason that it is the farthest east is because some of the Aleutian Islands cross the 180 degree line of longitude.  This places those islands in the eastern hemisphere; therefore, they are east of the Prime Meridian.  If this question is referring to the lower 48 states, then the answer changes.  The state that is located farthest east among the 48 contiguous states is Maine.  The eastern edge of Maine is 66 degrees west.  Sail Rock just off the coast from the West Quoddy Head Lighthouse is also part of Maine and technically even farther east.  

What is the message of the story "The Open Window"?

One message to the reader of "The Open Window" is that it is often difficult to decipher the truth in a person's narrative about an incident. Moreover, those who possess such talent of being able to weave cleverly deceptive tales can easily manipulate others.

Vera, whose name suggests truth, possesses the "specialty" to create  "[R]omance at short notice." Her talent lies in her ability to identify susceptibilities in her audience and then blur the lines...

One message to the reader of "The Open Window" is that it is often difficult to decipher the truth in a person's narrative about an incident. Moreover, those who possess such talent of being able to weave cleverly deceptive tales can easily manipulate others.

Vera, whose name suggests truth, possesses the "specialty" to create  "[R]omance at short notice." Her talent lies in her ability to identify susceptibilities in her audience and then blur the lines between reality and creativity in order to weave her tale so that it will have disturbing effects upon her listener(s).

When she is sent to entertain Mrs. Sappleton's guest, Framton Nuttel, Vera first ascertains whether he is acquainted with the area or anyone living there. When Nuttel replies that he knows "[H]ardly a soul," Vera immediately recognizes that she can unleash her spectacular imagination and weave a gothic tale of her uncle and cousins' having been lost in a bog with such verve that it will both captivate and, then, as its denouement becomes reality, terrify the neurotic guest.

Prove`log_(1/p) x = -log_p (x) (x > 0)`. I understand that if I flip the base `1/p` to `p` I'll get `-log_p (x)`. But how do I prove it?

Hello!

We want to prove the identity  `log_(1/p)(x) = -log_p(x)`  (for all `xgt0,` `pgt0` and `p != 1` ).

To do this, let's recall what logarithms are. By the definition,  `log_b(a)` is such a number `c` that  `b^c = a.`  It is known that such a number always exists and is unique (of course for `agt0,` `bgt0` and `b != 1` ).

Therefore to verify this identity we raise `1/p` to the power of each side:

...

Hello!

We want to prove the identity  `log_(1/p)(x) = -log_p(x)`  (for all `xgt0,` `pgt0` and `p != 1` ).

To do this, let's recall what logarithms are. By the definition,  `log_b(a)` is such a number `c` that  `b^c = a.`  It is known that such a number always exists and is unique (of course for `agt0,` `bgt0` and `b != 1` ).

Therefore to verify this identity we raise `1/p` to the power of each side:

`(1/p)^(log_(1/p)(x)) = (1/p)^(-log_p(x))`

(the function `(1/p)^x` is one-to one on its domain, therefore this operation gives an equivalent equality).

The left part is equal to `x` by the definition of logarithm, what about the right part? We'll use some properties of powers, `1/p=p^(-1)` and `(p^a)^b=p^(a*b):`

`(1/p)^(-log_p(x)) =(p^(-1))^(-log_p(x)) =p^((-1)*(-log_p(x))) =p^(log_p(x)).`

And this is equal to `x,` too, by the definition of logarithm. This way we proved the desired identity.

What words does the author use to avoid repeating "the road"?

One thing that Robert Frost does to avoid using the word "road" over and over again throughout this poem is to use pronouns instead of "road." For example, line five is as follows:

To where it bent in the undergrowth

"It" refers to one of the two roads. This pronoun is used again in line eight. In line ten, the narrator uses "them" instead of "roads."

For much of the rest of the poem, Frost...

One thing that Robert Frost does to avoid using the word "road" over and over again throughout this poem is to use pronouns instead of "road." For example, line five is as follows:

To where it bent in the undergrowth

"It" refers to one of the two roads. This pronoun is used again in line eight. In line ten, the narrator uses "them" instead of "roads."

For much of the rest of the poem, Frost substitutes various other words to stand-in for "road." The stand-in word is more often than not meant to be followed by the word "road," but Frost simply avoids using the word "road" and lets readers assume that the road is what he is talking about. For example, let's look at lines two and four:  

And sorry I could not travel both [roads]

And be one traveler, long I stood

And looked down one [road] as far as I could

Frost does this dropping of "road" a few more times in the poem. Lines six, eleven, and thirteen do the same thing.  

Finally, in line nineteen, the narrator substitutes "road" for the word "one."

I took the one less traveled by

Explain the roles and actions of different levels of government in relation to trade.

I am assuming that your question is about United States government and relates to international trade, not trade within the United States.  The only level of government that has control over the United States trade with foreign nations is the federal government, as mandated by the Constitution. Other levels of government have no power at all. 

Article I, Section 8 states that Congress regulates commerce with other countries.  There are a few different options that...

I am assuming that your question is about United States government and relates to international trade, not trade within the United States.  The only level of government that has control over the United States trade with foreign nations is the federal government, as mandated by the Constitution. Other levels of government have no power at all. 

Article I, Section 8 states that Congress regulates commerce with other countries.  There are a few different options that can be exercised in foreign trade.  One is to impose a tariff on in-coming goods, which makes them more expensive for Americans to buy, thus encouraging people to buy American-made goods instead.  This runs the risk of other nations doing the same, which means that fewer people will buy American-made goods. Another option is to have no tariff at all, which is pure "free trade," so that goods move freely over borders without any taxation.  Finally, an embargo can be imposed, which is generally done for political reasons, although one could certainly be imposed for a situation in which unsafe products from other countries were being sold.  We have had an embargo against Cuban products for a very long time. And while no one discusses this, I am sure that we are not supposed to be purchasing any goods from North Korea.

State and local governments are not permitted to enter into trade agreements with foreign countries, and it is easy to see why.  It would destroy the cohesion of the country.  If New York had a trade agreement with France, and Pennsylvania imposed tariffs upon French goods, it would be a disaster.  French goods would be routinely smuggled from New York to Pennsylvania. And that is just one small example.  To be a nation, there must be one cohesive policy that covers all the states. 

None of this stops anyone in any state from selling to or buying from other countries. It simply means that whatever rules apply to the situation, they have been decided upon by Congress, and they apply to all the states.

In the story of "The Best Girlfriend You Never Had," analyze Lucy's relationship with her father, mother, and Leo in detail to find evidence that...

Lucy's relationship with Leo is not healthy. Though they spend time together and read poetry to each other, Leo is not in love with Lucy but with a woman called Guenevere, but Guenevere does not seem to know that Leo exists and forgets him after meeting him. However, Leo says that Guenevere's dismissive behavior "adds to what he calls her charming basket of imperfections." He only likes women who don't like him back, making his relationship...

Lucy's relationship with Leo is not healthy. Though they spend time together and read poetry to each other, Leo is not in love with Lucy but with a woman called Guenevere, but Guenevere does not seem to know that Leo exists and forgets him after meeting him. However, Leo says that Guenevere's dismissive behavior "adds to what he calls her charming basket of imperfections." He only likes women who don't like him back, making his relationship with Lucy strange and unfulfilling. 

Lucy's relationships with her parents, who are alcoholics, is troubled. She says that she and Leo used to eat dinner "on TV trays next to our parents and their third martinis, watching What’s My Line and To Tell the Truth on television and talking about anything on earth except what was wrong." Lucy's family life is filled with a lot of drinking and not a lot of love or honesty. Her favorite childhood memory is when she pulled a heavy urn on top of herself when she was four and crushed both of her femurs. She recalls her stay in the hospital:

"My parents, when they came to visit, were always happy to see me and usually sober. I spent the remaining years of my childhood fantasizing about illnesses and accidents that I hoped would send me to the hospital again."

The only time her parents paid attention to her was the time she was in the hospital as a little girl, and she sadly prayed while growing up to have another accident so her parents would focus on her and love her. Her parents did not provide her with a lot of acceptance or love, and when she asked her father if he approved of Jeffrey, one of her boyfriends she hoped her parents would like, her father said, “Lucille...I haven’t ever liked any of your boyfriends, and I don’t expect I ever will. So why don’t you save us both the embarrassment, and not ask again.” Her parents rarely gave her the affection and attention she craved, as they were involved mainly with drinking.

The emergence of the Atlantic world can be seen as a cause of new developments and the result of historical processes. What long-term political,...

European countries were motivated to expand in part because of political competition among themselves and the economic theory of mercantilism, which sought to maximize a country's exports and minimize imports in an effort to amass bullion (or gold). New World conquests helped European countries export more and import less because the New World was a source of raw materials and markets for finished goods made in Europe. Nationalism, or the belief that a country's destiny...

European countries were motivated to expand in part because of political competition among themselves and the economic theory of mercantilism, which sought to maximize a country's exports and minimize imports in an effort to amass bullion (or gold). New World conquests helped European countries export more and import less because the New World was a source of raw materials and markets for finished goods made in Europe. Nationalism, or the belief that a country's destiny is to expand, also was a political motivation for European expansion. In addition, the growth of European populations was a demographic factor behind their expansion. 

As a result of the interconnectedness of the Atlantic World, there was an exchange of products, technology, and livestock. For example, horses were introduced into the New World from Europe, and agricultural products such as tobacco and sugar were brought back to Europe, where they proved very popular. Technologies such as guns were introduced in the New World, as were diseases that were unknown in the Western Hemisphere up to that point, including small pox. These diseases resulted in the decimation of some New World populations. Tragically, slavery was also introduced in the New World, as slaves were imported from Africa to the West Indies and to the mainland North American and South American colonies.

`f(x)=sqrt(x) ,n=3,c=4` Find the n'th Taylor Polynomial centered at c

Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)`  centered at `x=c.`  The general formula for Taylor series is:

`f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n`

or

`f(x) = f(c) + f'(c) (x-c)+ (f'(c))/(2!) (x-c)^2+ (f'(c))/(3!) (x-c)^3+ (f'(c))/(4!) (x-c)^4+...`

 To evaluate the given function `f(x) =sqrt(x)` , we may express it in terms of fractional exponent. The function becomes:

`f(x) = (x)^(1/2)` .

Apply the definition of the Taylor series by listing the `f^n(x) ` up to `n=3.`

 We determine each derivative using Power Rule for differentiation: `d/(dx) x^n = n*x^(n-1)` .

`f(x) = (x)^(1/2)`

`f'(x) = 1/2 * x^(1/2-1)`

          `= 1/2x^(-1/2) or1/(2x^(1/2) )`

`f^2(x) = d/(dx) (1/2x^(-1/2))`

         `= 1/2 * d/(dx) (x^(-1/2))`

         `= 1/2*(-1/2x^(-1/2-1))`

         `= -1/4 x^(-3/2) or -1/(4x^(3/2))`

`f^3(x) = d/(dx) (-1/4x^(-3/2))`

          `= -1/4 *d/(dx) (x^(-3/2))`

          `= -1/4*(-3/2x^(-3/2-1))`

          `= 3/8 x^(-5/2) or 3/(8x^(5/2))`

Plug-in `x=4` , we get:

`f(x) = (4)^(1/2)`

         `= 2`

`f'(4)=1/(2*4^(1/2))`

         `=1/(2*2)`

         `=1/4`

`f^2(4)=-1/(4*2^(3/2))`

          `= -1/(4*8)`

         ` = -1/32`

`f^3(4)=3/(8*4^(5/2))`

          `= 3/(8*32)`

          `= 3/256`

Applying the formula for Taylor series centered at `c=4` , we get:

`sum_(n=0)^3 (f^n(4))/(n!)(x-4)^n`

   ` =f(4) + f'(4) (x-4)+ (f'(4))/(2!) (x-4)^2+ (f'(4))/(3!) (x-4)^3`

   ` =2+ (1/4) (x-4)+ (-1/32)/(2!) (x-4)^2+ (3/256)/(3!) (x-4)^3 `

   ` =2+ (1/4) (x-4)+ (-1/32)/(2!) (x-4)^2+ (3/256)/(3!) (x-4)^3 `

   ` =2+ 1/4 (x-4)-1/(32*2) (x-4)^2+ 3/(256*6) (x-4)^3 `

   `=2+ 1/4 (x-4)-1/64 (x-4)^2+ 3/1536 (x-4)^3`

   `=2+ 1/4 (x-4)-1/64 (x-4)^2+ 1/512 (x-4)^3 `

The Taylor polynomial of degree `n=3`  for the given function `f(x)=sqrt(x)`  centered at ` c=4`  will be:

`P(x) =2+ 1/4 (x-4)-1/64 (x-4)^2+ 1/512 (x-4)^3 `

What is Margot likely to do after she is let out at the end of "All Summer in a Day"?

The story does not tell us how Margot will act after she emerges from the closet. However, we can probably make some speculations about her likely actions after she is let out.

First, Margot is likely to be very angry. After all, the sun only comes out once every seven years in Venus. We know that Margot, more than any of the other children, has been looking forward to seeing the sun. 

The text tells...

The story does not tell us how Margot will act after she emerges from the closet. However, we can probably make some speculations about her likely actions after she is let out.

First, Margot is likely to be very angry. After all, the sun only comes out once every seven years in Venus. We know that Margot, more than any of the other children, has been looking forward to seeing the sun. 

The text tells us that Margot desperately tried to dissuade the children from their cruel errand. We also learn that she threw herself against the door and beat on it after she was locked in. So, Margot is likely to be very angry after she is let out.

Second, although it is possible to guess Margot's emotional condition, it is difficult to predict Margot's likely actions upon emerging from the closet. Her anger may remain dormant or even hidden from the children. From the text, we learn that Margot is naturally introverted and that she is habitually wary during her interactions with the other children. She often says very little, even when her patience has been sorely tested.

When William pushes her, she does not push back. Even when the children accuse her of lying about her experiences with the sun, Margot remains characteristically silent.

However, Margot does occasionally have emotional outbursts; the text tells us that she once refused to take a shower at school and that she screamed at the thought of water touching her head. So, at this point, we can speculate about Margot's emotions after emerging from the closet. However, it may be a little harder to predict how she will act out her anger. 

Analyze prison and war in Gods Go Begging, and compare and contrast them in relation to social death. Make sure to quote the text and closely...

When Jesse visits the 7th floor of the prison, where everyone is forced to lie down, he reflects that "all of the inhabitants lived in a position that was at total odds with the rest of the world, perpetually perpendicular to the working men and women on the floors and streets beneath them." The physical position of the prisoners is a symbol of their displacement and their separation from everyday life. Véa writes of the...

When Jesse visits the 7th floor of the prison, where everyone is forced to lie down, he reflects that "all of the inhabitants lived in a position that was at total odds with the rest of the world, perpetually perpendicular to the working men and women on the floors and streets beneath them." The physical position of the prisoners is a symbol of their displacement and their separation from everyday life. Véa writes of the prisoners that when they get out of prison, "their souls and futures would be unchanged, while the world around them had evolved and gone on" (53). He compares the men in the prison ward to space travelers who travel in suspended animation and return to earth to find that everyone has changed around them. When they are released from jail, they will no longer be able to relate to others, so prison is a form of social death. 

Véa also implies that the war, like prison, causes people to be out of joint and makes them live a kind of social death. For example, Jesse is thinking about his time fighting in Vietnam and recalls seeing a photographer from the Army publication Stars and Stripes coming across a charred child. The photographer considers taking a close shot and then "finally gave into the reality of his constituency and backed away to take a long, sterile shot. His newspaper was not interested in photojournalism, only in raw numbers and morale-boasting photos" (75). The long shot that the photographer takes in this chilling passage is symbolic of the way in which the press doesn't capture the reality of what is going on in Vietnam. Only the soldiers on the ground, such as Jesse, know the reality of the war, and when they return to the United States, the nightmares about the war haunt them, causing them to live in social isolation from others. 

How does Keats exploit meter, rhyme and other litterary devices to serve and construct meaningn in his poem?

     The meter used in “To Autumn” is iambic pentameter, which means that each line of the poem is comprised of five iambic feet (unstressed syllable followed by a stressed syllable). For example, “With fruit the vines that round the thatch-eves run.” When reading the poem out loud, it becomes apparent that iambic pentameter creates a specific rhythm and natural flow to the poem. Keats may have chosen this rhythm to signify on the...

     The meter used in “To Autumn” is iambic pentameter, which means that each line of the poem is comprised of five iambic feet (unstressed syllable followed by a stressed syllable). For example, “With fruit the vines that round the thatch-eves run.” When reading the poem out loud, it becomes apparent that iambic pentameter creates a specific rhythm and natural flow to the poem. Keats may have chosen this rhythm to signify on the rhythm of nature and to support some of the images he presents in the poem such as “Thy hair soft-lifted by the winnowing wind” or “Among the river sallows, borne aloft.”

     In the first stanza of the poem, Keats uses ABAB rhyme pattern followed by CDEDCCE. In the second and third stanza, he uses the rhyme pattern CDECDDE. The shift from the very regular and monotonous rhyme pattern ABAB to a somewhat more complex rhyme pattern aligns with the meaning the poem tries to convey; namely that as summer is coming to a close, nature changes.

     Keats uses several literary and stylistic devices to convey meaning. For example, he uses alteration (“lambs loud”) to draw attention to images of autumn created in the poem. He also uses rhetorical questions (“Where are the songs of spring? Ay, Where are they?”) to invite the reader to behold and contemplate nature as it changes in fall. Last but not least, there are several instances of anthropomorphism in the poem (“And still more, later flowers for the bees / Until they think warm days will never cease”) to convey the notion that nature and its creatures are living sentient beings.    

What is the mood of “The Stolen Party” by Liliana Heker?

The story has a general mood of sadness. It is sad to see Rosaura’s dreams crushed at the end of the story, when she does not receive a present, like the other children who attend Luciana’s party. This goes on to confirm what her mother has been trying to tell her, that Luciana does not consider her a friend, rather, the daughter of their maid.

It is heartbreaking that in spite of Rosaura’s great contribution...

The story has a general mood of sadness. It is sad to see Rosaura’s dreams crushed at the end of the story, when she does not receive a present, like the other children who attend Luciana’s party. This goes on to confirm what her mother has been trying to tell her, that Luciana does not consider her a friend, rather, the daughter of their maid.

It is heartbreaking that in spite of Rosaura’s great contribution to the party—made out of love for Luciana’s family—she is still not considered Luciana’s friend. When Senora Ines says “What a marvelous daughter you have, Herminia,” Rosaura beams with pleasure and expects to be given presents, just like the other children before her. When Senora Ines hands over two bills, from her purse to Rosaura and her mother, Rosaura’s “arms stiffen” and she “presses herself against her mother’s body”, with her “cold clear eyes fixed” on Senora Ines’s face.

Also, one can’t help being angry at society for the kind of social biases it passes on to innocent children. Clearly, Rosaura is innocent of any biases, as she refuses to believe her mother’s opinions about the rich. She “thought it unfair of her mother to accuse other people of being liars simply because they were rich”. Though she is encouraged to do things that the other children do not do, such as collecting party things to and from the kitchen or passing the cake around, she does not understand that she is expected to do these things because she is “different” from the other children. It is as if she is being prepared for a future as a maid.

How does the calculated omission of Miss Brill's first name contribute to her characterization?

Miss Brill imagines herself to be quite a proper lady.  She decided to wear her fur, a "Dear little thing!" for her Sunday out to the park to hear the band play.  She likes to sit and watch the people around her, eavesdropping on their conversations, all the while pretending disinterest.  She watches the crowds, couples and groups stopping to talk, some buying handfuls of flowers, and the children, dressed in their Sunday best.  To...

Miss Brill imagines herself to be quite a proper lady.  She decided to wear her fur, a "Dear little thing!" for her Sunday out to the park to hear the band play.  She likes to sit and watch the people around her, eavesdropping on their conversations, all the while pretending disinterest.  She watches the crowds, couples and groups stopping to talk, some buying handfuls of flowers, and the children, dressed in their Sunday best.  To her, it all seems to feel so bright and cheerful and interesting.  "Oh, how fascinating it was!  How she enjoyed it!  How she loved sitting here, watching it all!"  After she's seen her fill, she typically stops at the bakery on the way home to buy a piece of cake.  All along, she's called Miss Brill and never by a first name: this choice adds to the sense of formality with which she conducts herself.  She never involves herself in conversation with anyone else at the park; she remains apart, aloof.  The deliberate omission of her first name adds to the elegance, with her fur and her almond cake, that Miss Brill seems to believe she possesses. (This is partly why she is so devastated to be the butt of the young couple's jokes.)

In Martin Luther King Jr.'s "I Have a Dream" speech, what is an example of repetition? What is its effect?

There are many examples of repetition in Martin Luther King Junior's "I Have a Dream" speech. The repetition serves as emphasis. Since the speech was given orally, the repetition also helps the audience comprehend his points. It is often more difficult to just hear information than it is to read or have visual aids, so the repetition helps the audience track with the speech and King's tenets. In the example below, King repeats the phrase...

There are many examples of repetition in Martin Luther King Junior's "I Have a Dream" speech. The repetition serves as emphasis. Since the speech was given orally, the repetition also helps the audience comprehend his points. It is often more difficult to just hear information than it is to read or have visual aids, so the repetition helps the audience track with the speech and King's tenets. In the example below, King repeats the phrase "one hundred years later" three times. This serves to highlight the fact that it has been a century since Lincoln signed the Emancipation Proclamation, which freed the slaves, yet black people were still in a type of bondage. 

But one hundred years later, the Negro still is not free. One hundred years later, the life of the Negro is still sadly crippled by the manacles of segregation and the chains of discrimination. One hundred years later, the Negro lives on a lonely island of poverty in the midst of a vast ocean of material prosperity. One hundred years later, the Negro is still languished in the corners of American society and finds himself an exile in his own land. And so we've come here today to dramatize a shameful condition.

Perhaps the most famous example of repetition in this speech is the phrase, "I have a dream." King repeats this phrase as he develops an idea of what his dream entails. It becomes a type of anthem as he paints a picture of a country in which there is unity and equality among races. 

I have a dream that one day even the state of Mississippi, a state sweltering with the heat of injustice, sweltering with the heat of oppression, will be transformed into an oasis of freedom and justice.

I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character.

I have a dream today!

Another noteworthy example of repetition in this speech is the repeated phrase "let freedom ring." This phrase is repeated 10 times and is a rallying cry. He uses it to proclaim that freedom, as it is expressed in the song "My Country 'Tis of Thee," will only be fully realized when there is equality among all races of people. So he repeats the phrase and calls out many different locations in the country. The locations he mentions span the whole country and creates a cry for unification.  

What is postmodernism? What is post-structuralism?

Postmodernism is, by its very nature, difficult to define since it basically amounts to a rejection of traditional categories of knowledge. Basically, postmodernists call any universal truth, narrative, or point of consensus into question. They argue that our experiences and understandings are subjective because each person comes to these understandings from their own perspective. In history, for example, postmodernists would argue first that modern people cannot really understand the motives and perspectives of historical actors,...

Postmodernism is, by its very nature, difficult to define since it basically amounts to a rejection of traditional categories of knowledge. Basically, postmodernists call any universal truth, narrative, or point of consensus into question. They argue that our experiences and understandings are subjective because each person comes to these understandings from their own perspective. In history, for example, postmodernists would argue first that modern people cannot really understand the motives and perspectives of historical actors, calling all historical interpretation into question. Second, they claim that there can be no grand narrative of history because there are too many perspectives involved in any historical moment. Basically, postmodernists, whose work has informed almost every academic discipline, question the very assumptions disciplines are based on. 

Post-structuralism also tends to focus on the individual and denies the authority of academic disciplines—especially texts. One of the major ideas associated with post-structuralism is the notion that texts (nonfiction or fiction) cannot have a fixed meaning independent of the reader's interpretation of them. Accordingly, the reader is as important in assigning meaning to texts as the author. In his famous essay "The Death of the Author," Roland Barthes, one of several literary critics closely associated with post-structuralism, claimed provocatively that the "source, [the] voice" of a text "is not to be located. . . this is because the true locus of writing is reading." As a result, he claimed that post-structuralism heralded the "death" of the author because the reader created meaning as much as the author.

Proponents of post-structuralism in particular are notorious for being difficult to read for anyone other than an academic specialist. Despite this, their work, along with that of the postmodernists, has been influential in literary criticism, history, and many other fields. 

In O. Henry's "The Ransom of Red Chief," how do the criminals change?

When someone changes his or her thoughts or feelings in a dramatic way from the beginning of a story to the end, he or she is called a dynamic character. In O. Henry's "The Ransom of Red Chief," both of the criminals, Bill and Sam, learn a lesson that changes their minds about the benefits and lucrativeness of kidnapping. For example, at the beginning when they decide to kidnap a child to make a quick...

When someone changes his or her thoughts or feelings in a dramatic way from the beginning of a story to the end, he or she is called a dynamic character. In O. Henry's "The Ransom of Red Chief," both of the criminals, Bill and Sam, learn a lesson that changes their minds about the benefits and lucrativeness of kidnapping. For example, at the beginning when they decide to kidnap a child to make a quick buck, the reasoning behind their thinking is as follows:

"Philoprogenitiveness, says we, is strong in semirural communities; therefore, and for other reasons, a kidnapping project ought to do better there than in the radius of newspapers that send reporters out in plain clothes to stir up talk about such things."

First of all, the word philoprogenitiveness is a noun that describes parents' strong love for their children. Thus, the criminals believe that parents in a rural community would pay any amount in order to get back a kidnapped child. These men haven't met the Dorsets, though. After a couple of days with Johnny Dorset, the criminals learn that not all parents will pay anything for the safe return of children. They also learn that kidnapping is neither beneficial to their health, nor is it lucrative. Johnny does some of the following things to change Bill and Sam's minds about kidnapping: 

• When offered candy, Johnny throws a piece of a brick at Bill's eye.


• He fights "like a welterweight cinnamon bear."


• He likes camping out and doesn't want to go home.


• He almost scalps Bill and threatens to burn Sam at the stake.


• He puts a hot potato down Bill's back and stomps on it with his foot.


• He throws rocks that hit Bill in the head.


• He plays horsey with Bill and rides him all day long. 

Bill is the first to show signs of being a dynamic character when he tells Sam the following:

"You know, Sam . . . I've stood by you without batting an eye in earthquakes, fire, and flood--in poker games, dynamite outrages, police raids, train robberies, and cyclones. I never lost my nerve yet till we kidnapped that two-legged skyrocket of a kid."

Fortunately for them, Mr. Dorset knows that the kidnappers will discover what a handful their son is and want to return him. Ironically, and to the kidnappers' relief, Mr. Dorset offers them a way out of their own scheme. The culminating event that proves that the criminals have changed their minds about kidnapping Johnny is when they pay Mr. Dorset $250 to give the boy back rather than making any money. By paying Mr. Dorset, the criminals admit defeat and demonstrate that they have changed their minds about the benefits of the kidnapping scheme.

How did the printing press transform both the private and public lives of Europeans?

Johannes Gutenberg's printing press, invented around 1440 in the midst of the Renaissance, gave people more access to written literature, including religious texts and political pamphlets.

Previously, literacy had been limited to members of the clergy, the aristocracy, and members of the merchant class. The printing press expanded the possibilities for people who had not previously had opportunities to learn to read.

The Protestant Reformation would not have happened without the printing press. In 1517,...

Johannes Gutenberg's printing press, invented around 1440 in the midst of the Renaissance, gave people more access to written literature, including religious texts and political pamphlets.

Previously, literacy had been limited to members of the clergy, the aristocracy, and members of the merchant class. The printing press expanded the possibilities for people who had not previously had opportunities to learn to read.

The Protestant Reformation would not have happened without the printing press. In 1517, Martin Luther posted his 95 Theses on the door of the Wittenberg Castle Church. His list of grievances against the indulgences of the Catholic Church was soon published and distributed as a result of the printing press.

Gutenberg's press also allowed for the Bible to be printed and distributed for private use. Previously, worshipers were beholden to clergymen to explain to them what the Bible said and what Scripture meant. Now, Christians were able to read the Bible for themselves and interpret its meaning. This personal relationship with Scripture was a key aspect of the Protestant Reformation.

In the eighteenth-century the printing press would be used to print and distribute political pamphlets, such as Thomas Paine's Common Sense. Ideas such as Paine's would be key to the Enlightenment, which would later inspire the major Atlantic revolutions: the American Revolution, the French Revolution, and the uprising in Haiti.

Access to printed information enriched people's lives. They could enjoy literature, create a more personal relationship with God, and read political ideas. The printing press allowed people to consider what they thought about the world, thus allowing them to engage with it more constructively.

In "Young Goodman Brown," what social institutions do Deacon Gookin, Goody Cloyse, and the minister represent?

When the devil points out Goody Cloyse on the path, young Goodman Brown notes that she is the elderly woman of unimpeachable reputation in town who taught him his catechism when he was young; in fact, she is still, along with the minister and Deacon Gookin, a spiritual advisor for Brown.  These three people, jointly, represent the church.  They are all thought to be beyond moral reproach, and they are responsible for helping to lead...

When the devil points out Goody Cloyse on the path, young Goodman Brown notes that she is the elderly woman of unimpeachable reputation in town who taught him his catechism when he was young; in fact, she is still, along with the minister and Deacon Gookin, a spiritual advisor for Brown.  These three people, jointly, represent the church.  They are all thought to be beyond moral reproach, and they are responsible for helping to lead the community down a righteous path.  It is very ironic, then, that Brown spots Goody Cloyse, and later hears the deacon and minister, on the path because he would never have expected them to be on their way to the witches' Sabbath.  They are the community's best examples of morality, and so if even they are in league with the devil, it seems that there can be little hope, if any, for anyone else to maintain innocence.

Their guilt also seems like an indictment of Puritan society by Hawthorne.  If even the most moral folks in this community are corrupt, then that says nothing positive about Puritans: instead, they seem hypocritical and false.

What does Motivation mean? |

Asking "what is Motivation?" is equal to asking about happiness, satisfaction, and even sadness. It is entirely up to the individual's life experiences. Evidence of this is the fact that there are a myriad of theories, not "laws," that define motivation. As such, it remains a philosophical debate.

• The Dual Factor theory by Hertzberg

This theory says that there are two ways to be motivated: One, is the basic factor of liking what you are doing, or your environment, your co-workers, and so on. Those are, what he calls, the motivating.

The second, is what he calls the hygiene factors. This entails the opposite of the motivating factors. These are the factors that, if they are not good enough, they will be "cleaned out" by the individual. Examples are: salary, benefits, policies, and people.

• Maslow's Hierarchy of Needs

This theory dates back to a 1943 paper, written by Abraham Maslow. While motivation is nowhere in the hierarchy, Maslow states that, in order to do anything, one must have, a) safety, b) security, c) health. Those would be the motivating factors to exert a new action. In a way, motivators equate "needs." We need motivation first, in order to conduct an action. Motivation is everything.

• Expectancy

This motivation theory relies on basic conditioning. We behave however it fits us best. The motivation is the outcome: for example, if you want to make money, then work harder. If you want to earn the trust of your boss, stay later at work and develop good listening skills in the event that he or she needs to make a friend.

The three factors of motivation in this theory are: expectancy, instrumentality, and valence. In the example given above, the expectancy would be the trust of your boss. The instrumentality would be you, staying later at work to seize the chance to be a sounding board to your boss if he or she needs support. The valence is the end-result: to earn their trust.

As there are other theories (check links included), you will find that the main factors are that a) we need to be of sound of mind and body, b) we need to have a goal in mind, and c) we need to have a way to get it. That is, basically, what motivation means.

What are the arguments that were put forward against the change of the social services 1946 referendum in Australia?

The 1946 Constitutional referendum in Australia defined the ability of the legislative branch to pass laws related to social services, including unemployment insurance, allowances for pregnant women and widows, medical services, pharmaceutical aid, and benefits for students. Many of these social services already existed in Australia prior to the referendum, but its passage clarified the extent to which the government could provide aid, and made the existence of the laws constitutional. One concern about the...

The 1946 Constitutional referendum in Australia defined the ability of the legislative branch to pass laws related to social services, including unemployment insurance, allowances for pregnant women and widows, medical services, pharmaceutical aid, and benefits for students. Many of these social services already existed in Australia prior to the referendum, but its passage clarified the extent to which the government could provide aid, and made the existence of the laws constitutional. One concern about the expansion of social services powers was the increase of revenue granted to the Commonwealth relative to the states; in 1942, the Commonwealth became the sole government entity responsible for collecting income tax, taking some responsibility away from the states. Some Australians were concerned about the increasing centralization of taxation, especially when the Commonwealth increased taxes to allow benefits for the sick and unemployed. Another argument against the referendum was that the increase in autonomy granted to the Commonwealth would subvert its constitutional role. Those against the referendum argued that it would grant the Commonwealth too much legislative power, in addition to providing it with an increase in tax revenue. Overall, the opponents of the 1946 referendum were primarily concerned about how it would provide both more tax income and more legislative power than the Constitution had allowed at the time, and promoted conforming to the Constitution's existing allowances rather than changing it to protect these new powers. However, the referendum passed with 54% of the vote, and the Constitution was amended.

What are the key points from chapters 22-27 in Harper Lee's To Kill a Mockingbird?

Chapter 22 of To Kill a Mockingbirdpicks up after Tom has been convicted of rape. The key event in this chapter is that they discover that Bob Ewell threatened Atticus and spat in his face. Another important event occurs in chapter 24 when we discover that Tom has been killed in an attempt to escape from prison. The appeal Atticus hopes to bring before a judge will never happen, and justice will never be...

Chapter 22 of To Kill a Mockingbird picks up after Tom has been convicted of rape. The key event in this chapter is that they discover that Bob Ewell threatened Atticus and spat in his face. Another important event occurs in chapter 24 when we discover that Tom has been killed in an attempt to escape from prison. The appeal Atticus hopes to bring before a judge will never happen, and justice will never be served for Tom. Atticus has the unenviable task of going to tell Tom's mother in chapter 25.

In chapter 27 we learn that Bob Ewell is still up to no good, and that he has not yet given up on avenging what he perceives as Atticus's attempt to humiliate his family in court. It is also announced that Scout will participate in a school pageant, dressed as a ham. This leads to a very important event in the novel, which occurs in chapter 28—Bob Ewell's fateful attack on the children on the way back from the pageant.

Attached are a question and the matlab code. The code gives the total surface area as 639.4828, but the figure is not showing up. Also, the...

i, j, k are unit vectors.

r(u,v)=(b+a*cos(u))*cos(v) i + (b+a*cos(u))*sin(v) j + a*sin(u) k

0<=u,v<=2pi and a=1/4 and b=1

The surface area is:

A=double integral of magnitude of (r_u x r_v) dA

r_u is the partial derivative of r(u,v) with respect to u and r_v with respect to v:

r_u(u,v)= -a*sin(u)*cos(v) i -a*sin(u)*sin(v) j +a*cos(u) k

r_v(u,v)= -(b+a*cos(u))*sin(v) i +(b+a*cos(u))*cos(v) j

Compute the cross product:

r_u x r_v = -a*cos(u)*(b+a*cos(u))*cos(v) i - a*cos(u)*(b+a*cos(u))*sin(v)...

i, j, k are unit vectors.

r(u,v)=(b+a*cos(u))*cos(v) i + (b+a*cos(u))*sin(v) j + a*sin(u) k

0<=u,v<=2pi and a=1/4 and b=1

The surface area is:

A=double integral of magnitude of (r_u x r_v) dA

r_u is the partial derivative of r(u,v) with respect to u and r_v with respect to v:

r_u(u,v)= -a*sin(u)*cos(v) i -a*sin(u)*sin(v) j +a*cos(u) k

r_v(u,v)= -(b+a*cos(u))*sin(v) i +(b+a*cos(u))*cos(v) j

Compute the cross product:

r_u x r_v = -a*cos(u)*(b+a*cos(u))*cos(v) i - a*cos(u)*(b+a*cos(u))*sin(v) j - a*(b+a*cos(u))*sin(u) k

Compute the magnitude:

magnitude(r_u x r_v)= sqrt(a^4*(cos(u))^2+2*a^3*b*cos(u)+a^2*b^2)= a*(b+a*cos(u))

Lastly, evaluate the integral:

integral(integral(a*(b+a*cos(u)),v,0,2*pi),u,0,2*pi) = 4*pi^2 * a * b

With a=1/4 and b=1 the surface area is pi^2.

The Matlab code for the plot is:

clear all
syms u v
a=1/4; b=1;
x=(b+a*cos(u))*cos(v);
y=(b+a*cos(u))*sin(v);
z=a*sin(u);
ezsurf(x,y,z,[0,2*pi,0,2*pi])

Who are the Magi in O. Henry's short story "The Gift of the Magi" and why?

O. Henry intrudes at the end of the narrative of his short story, "The Gift of the Magi," and declares that Della and Jim are the Magi. This young married couple is considered the Magi because, like the three kings who came to see the baby Jesus, they give valuable gifts unselfishly.

Despite the fact that O. Henry states that the Magi gave wise gifts and Jim and Della are "two foolish children who most...

O. Henry intrudes at the end of the narrative of his short story, "The Gift of the Magi," and declares that Della and Jim are the Magi. This young married couple is considered the Magi because, like the three kings who came to see the baby Jesus, they give valuable gifts unselfishly.

Despite the fact that O. Henry states that the Magi gave wise gifts and Jim and Della are "two foolish children who most unwisely sacrificed," he yet compares the young husband and wife to the Magi: 

Of all who give and receive gifts, such as they are wisest....They are the wisest.

While this statement seems paradoxical when considered with the previous one that they "unwisely sacrificed," nevertheless, Jim and Della are wise in the sense that they understand the value of love. For, no material possession is as important as the happiness of the beloved. This Jim and Della understand because they have sacrificed their personal treasures in order to make their beloved spouse happy. In this sense, then, they are "the wisest." Like the magi, they have given valuable treasures up to the beloved.  

Where does the internal perspective in A Passage to India become evident?

When Dr. Aziz approaches Old Callendar's house in chapter 2, his internal perspective becomes more evident. He knows that if he approaches the house in a tonga, a type of carriage, he might be turned away from the Englishman's house for acting too proud for an Indian. Forster writes, "his feelings—the sensitive edges of him— feared a gross snub." As Dr. Aziz waits for a message from Callendar, two Englishwomen come out and take his...

When Dr. Aziz approaches Old Callendar's house in chapter 2, his internal perspective becomes more evident. He knows that if he approaches the house in a tonga, a type of carriage, he might be turned away from the Englishman's house for acting too proud for an Indian. Forster writes, "his feelings—the sensitive edges of him— feared a gross snub." As Dr. Aziz waits for a message from Callendar, two Englishwomen come out and take his tonga without asking. He then thinks, "The inevitable snub—his bow ignored, his carriage taken." The women take his carriage without thanking him, and the reader is privy to his thoughts. He feels that he has been embarrassed and wronged, and he feels invisible in front of the Englishwomen who think everything they see belongs to them. 

Later in the chapter, Dr. Aziz enters a mosque where he meets Mrs. Moore for the first time. By this point, his internal perspective is very clear. The author conveys Dr. Aziz's feelings in the mosque in great detail in the following passage:

A mosque by winning his approval let loose his imagination. The temple of another creed, Hindu, Christian, or Greek, would have bored him and failed to awaken his sense of beauty. Here was Islam, his own country, more than a Faith, more than a battle-cry, more, much more. . . Islam, an attitude towards life both exquisite and durable, where his body and his thoughts found their home.

It is because the reader is allowed to feel Dr. Aziz's peace and his comfort in the mosque after being rebuffed by the other English people that the reader understands why Mrs. Moore's presence in the mosque rattles Dr. Aziz. Unlike the outside world, where he must be subservient to English people, Dr. Aziz feels that the mosque is his territory. He confronts Mrs. Moore in the mosque and says, "Madam, this is a mosque, you have no right here at all; you should have taken off your shoes; this is a holy place for Moslems." The reader has insight into the way Dr. Aziz feels at this point and understands his anger at an Englishwoman invading the place he feels is his sanctuary. 

What do Lily's jacket pockets symbolize in The Giver?

The pockets of Lily’s jacket symbolize her growing maturity. 

In Jonas’s community, the children all age at the same time in a special ceremony in December.  This is all part of maintaining Sameness.  There is a ceremony for each age group from One to Twelve.  At One, the babies get a name and a home.  At Twelve, the children are assigned their lifetime job and are no longer considered children.  They are adults in...

The pockets of Lily’s jacket symbolize her growing maturity. 

In Jonas’s community, the children all age at the same time in a special ceremony in December.  This is all part of maintaining Sameness.  There is a ceremony for each age group from One to Twelve.  At One, the babies get a name and a home.  At Twelve, the children are assigned their lifetime job and are no longer considered children.  They are adults in training. 

The ceremonies in between are smaller milestones.  Most of them have to do with growing independence and maturity.  For example, at age Nine children get bicycles so that they can venture into the community on their own.  The Eights get a smaller indication of trust. 

Jonas watched and cheered as Lily marched proudly to the stage, became an Eight and received the identifying jacket that she would wear this year, this one with smaller buttons and, for the first time, pockets, indicating that she was mature enough now to keep track of her own small belongings. (Ch. 6) 

Lily likely does not have many belongings, because no one really owns anything in Jonas’s society.  Everything is provided for them.  Jonas is even chastised for bringing an apple home instead of eating it right away.  Still, whatever she does have, she now has a pocket for. 

The fact that clothing is the same for everyone, and small designations like who has pockets are so important, is an indicator of the conformity in Jonas’s society.  Clothing indicates your age when you are a child and your status later in life.  Everything is a ritual.  Everything has a meaning and a purpose.  It keeps everyone working toward the same goal, and maintains Sameness.  Sameness keeps everyone safe, happy, and comfortable because everyone knows what to do and what to expect at all times.

Describe how the author develops the steps of the Hero's Journey.

The author follows the steps of the Hero’s Journey (a theme developed by Joseph Campbell in his book Hero with a Thousand Faces) in the frame story of Salamanca Tree Hiddle’s journey from Bybanks, Kentucky, to Euclid, Ohio, and on to Coeur d’Alene, Idaho.

The journey of a hero starts with humble beginnings. Sal is an only child of simple parents who live a simple life in Kentucky. She is content with her life...

The author follows the steps of the Hero’s Journey (a theme developed by Joseph Campbell in his book Hero with a Thousand Faces) in the frame story of Salamanca Tree Hiddle’s journey from Bybanks, Kentucky, to Euclid, Ohio, and on to Coeur d’Alene, Idaho.

The journey of a hero starts with humble beginnings. Sal is an only child of simple parents who live a simple life in Kentucky. She is content with her life (even if her mother is not). When her mother leaves, and Sal learns that she is not coming back, she is faced with the choice of the hero’s journey. Should she accept the fact and stay where she is, or should she deceive herself that there is some way that she can bring her back? She crosses the threshold and the real Hero’s Journey begins when she sets out on the road trip with her grandparents. She has trusty companions, as all heroes do (her grandparents, Phoebe, and Ben) who in one way or another help her on her way. She goes into the belly of the whale when her grandmother is bitten by a snake, which contributes to her eventual death. Sal learns from this and becomes stronger, beginning to accept the fact that those she loves can be lost. She reaches her goal when she stands over the wrecked bus where her mother died and finally accepts the truth when she sees her mother’s grave. She has been changed, even as she returns to her home, ready to recreate a new life without her mother.

How does Janie struggle to free herself from the power of Nanny, Joe, and Logan, and how does the author use this power struggle to enhance the...

Janie spends the grand majority of Zora Neale Hurston's Their Eyes Were Watching God attempting to find her own horizon.  She grows up under the hand of Nanny, a former slave who looks for little more in life than peace and security.  Because of Nanny's outlook, she guides Janie into what basically amounts to an arranged marriage with a man named Logan Killicks, an older farmer who, although rough around the edges, owns land and can provide for Janie.  However, the marriage is loveless. When Janie shares this information with Nanny and complains of her unhappiness, it upsets Nanny greatly.

Nanny sent Janie along with a stern mien, but she dwindled all the rest of the day as she worked. And when she gained the privacy of her own little shack she stayed on her knees so long she forgot she was there herself.  Towards morning she muttered, "Lawd, you know mah heart. Ah done de best Ah could do. De rest is left to you." She scuffled up from her knees and fell heavily across the bed. A month later she was dead.

Janie thought that love would eventually develop, but it never develops.  The relationship begins to devolve further when Logan begins to insist that Janie do more and more of the chores around the house.  Janie takes a stand, insulting Logan for both the way he treats her and for his appearance.  He gets very upset with Janie, and their relationship deteriorates.  Eventually, a man named Jody Starks comes walking down the road in front of the house, and Janie makes a point to try to get his attention.  They talk and hit it off, and Janie begins to see in Jody an opportunity to change her life.  At first, Janie's feelings are ambivalent: "Janie pulled back a long time because he [Jody] did not represent sun-up and pollen and blooming trees, but he spoke for far horizon. He spoke for change and chance."  This change is something Janie wants, and she eventually runs off with Jody to a town called Eatonville.

In Eatonville, Jody begins to establish himself.  He becomes mayor (after running uncontested), opens a store, and begins to buy Janie fancy things.  He wants her to look good. However he does this not so that she will feel good, but so people will see her and think more of him for the way he treats her.  Eventually his treatment of her devolves, as he wants her to been seen, but he does not want her to speak.  He then begins to berate her, and she loses hope of the opportunity that she thought would be part of her life with him.  He then begins to criticize her looks around the store, in front of other people, until one day when Janie retaliates, telling him, "When you pull down yo' britches, you look lak de change uh life."  This marks the breaking point in their relationship.  After being publicly humiliated in this way, Jody's health grows worse and worse, and he soon dies.  

After Jody's death, Janie continues to run the store, but she still feels unfulfilled until she meets a man named Tea Cake.  In Tea Cake, she finds the connection she has been looking for.  He treats her well and respects her, and even though they have some bumps in their relationship, she understands him. He helps her grow less callous and more compassionate.  She finds herself wanting to do things she avoided in the past.  While she detested the physical work that Logan expected of her, she willingly moves to the Florida Everglades and works alongside Tea Cake on "the muck."  Even though he cannot provide for her as Jody did, she is happy to be poor with him.  Although their relationship ends in an unfortunate tragedy, Janie is able to find her own horizon:

Here was peace. She pulled in her horizon like a great fish-net. Pulled it from around the waist of the world and draped it over her shoulder. So much of life in its meshes! She called in her soul to come and see.

Despite the toxic nature of most of her relationships, Janie was able to take something from each of them to help her become a capable and content woman.  Without her various struggles for power, Janie never would have discovered her own identity or learned that true power emerges through compromise.

What is the place of women in the Igbo society?

In Achebe's Things Fall Apart, the narrative mostly focuses on Okonkwo, a hyper-masculine tribal leader. He represents an extreme example of the Umuofian view of women and the role of women in their society.

Okonkwo has three wives, as is allowed in Umuofian culture. Women do not hold power in the tribe in terms of government or leadership. Men are allowed to beat their wives. Okonkwo, though, gets in trouble for hitting one of...

In Achebe's Things Fall Apart, the narrative mostly focuses on Okonkwo, a hyper-masculine tribal leader. He represents an extreme example of the Umuofian view of women and the role of women in their society.

Okonkwo has three wives, as is allowed in Umuofian culture. Women do not hold power in the tribe in terms of government or leadership. Men are allowed to beat their wives. Okonkwo, though, gets in trouble for hitting one of his wives during Peace Week. The other tribesmen agree that that beating is warranted; it is simply not allowed during that week. Therefore, most of the time, violence against women is condoned.

Okonkwo's attitude comes in part from his father. Okonkwo has a troubled relationship with his father, whom Okonkwo sees as lazy and unproductive; therefore, his father is not masculine. Okonkwo, on the other hand, is famous for his cultivation of yams, which "stood for manliness" (33) because a successful farmer is hard-working and a good provider. Okonkwo's obsession with manliness affects his relationships with his children as well. He feels closest to his daughter Ezinma, but she is lesser because she is a girl; he wishes she were born a boy instead. His son Nwyoe, on the other hand, is more sensitive and less manly than Okonkwo wants him to be.

About halfway through the novel, Okonkwo's masculinity is seriously questioned. He accidentally shoots and kills a man at a funeral celebration. The accidental nature of the act makes it a "feminine crime." This is obviously humiliating for Okonkwo. He is exiled to his motherland for seven years. While he is there, his mother's tribesmen point out to him that even though women are seen as less important in Umuofia, in Mbanta, "the mother is supreme" (134). This is because children look for sympathy from their mothers; the mother represents protection, which is important. The people of Mbanta emphasize the balance between male and female roles, while Okonkwo represents an extreme version of masculinity that is even beyond what his own tribespeople value or practice.

Why is the 10th Amendment to the US Constitution violated so much?

This seems to be a rather slanted question, assuming that the Tenth Amendment of the United States Constitution is violated almost routinely.  There are many who disagree with that assumption, including me.  Often, the federal government undertakes legislation or regulation in a way in which many people do not understand is perfectly in keeping with its enumerated powers.  For example, the interstate highway system is within Congress's purview because it is an important element of...

This seems to be a rather slanted question, assuming that the Tenth Amendment of the United States Constitution is violated almost routinely.  There are many who disagree with that assumption, including me.  Often, the federal government undertakes legislation or regulation in a way in which many people do not understand is perfectly in keeping with its enumerated powers.  For example, the interstate highway system is within Congress's purview because it is an important element of national defense.  If troops cannot be moved efficiently, they are completely ineffective.  Another example is the minimum wage.  I hear people complain that is unconstitutional sometimes.  But in fact, setting the minimum wage is part of interstate commerce.  Much anti-discrimination legislation is in the power explicitly given to Congress under the Fourteenth Amendment.  The enumerated powers of the federal government are broad mandates that include a great deal more power than people realize. Even though education is not listed as a congressional mandate, there is an argument to be made that education is part of national security and commerce as well.  Without an educated workforce, we cannot properly defend ourselves or compete in a global economy.  When the federal government does overreach and violates the Tenth Amendment, the Supreme Court is there to deal with that, and thus far, most of the instances that I hear people complaining have been upheld as perfectly proper within the confines of the Constitution.

`f(x) = arcsec(2x)` Find the derivative of the function

The given function: `f(x) =arcsec(2x) ` is in a form of an inverse trigonometric function. 

For the derivative formula of an inverse secant function, we follow:

`d/(dx)(arcsec(u))=((du)/(dx))/(|u|sqrt(u^2-1))`

To be able to apply the formula, we let u` =2x` then` u^2 = (2x)^2=4x^2` and

`(du)/(dx) = 2` .

It follows that `f(x) =arcsec(2x)` will have a derivative of:

`f'(x) = 2/(|2x|sqrt((2x)^2-1))`

`f'(x) = 2/(|2x|sqrt(4x^2-1))`

Cancel out common factor 2 from top and bottom:

`f'(x) = 1/(|x|sqrt(4x^2-1))`

...

The given function: `f(x) =arcsec(2x) ` is in a form of an inverse trigonometric function. 

For the derivative formula of an inverse secant function, we follow:

`d/(dx)(arcsec(u))=((du)/(dx))/(|u|sqrt(u^2-1))`

To be able to apply the formula, we let u` =2x` then` u^2 = (2x)^2=4x^2` and

`(du)/(dx) = 2` .

It follows that `f(x) =arcsec(2x)` will have a derivative of:

`f'(x) = 2/(|2x|sqrt((2x)^2-1))`

`f'(x) = 2/(|2x|sqrt(4x^2-1))`

Cancel out common factor 2 from top and bottom:

`f'(x) = 1/(|x|sqrt(4x^2-1))`

This can also be written as :` f'(x)= 1/(sqrt(x^2)sqrt(4x^2-1))` since

`|x| = sqrt(x^2)`

Then applying the  radical property:` sqrt(a)*sqrt(b)= sqrt(a*b)` at the bottom, we get:

`f'(x) = 1/sqrt(x^2*(4x^2-1))`

`f'(x) = 1/sqrt(4x^4 -x^2)`

The derivative of the function f(x) =arcsec(x) can be :

`f'(x)= 1/(|x|sqrt(4x^2-1))`

 or  `f'(x)= 1/(sqrt(x^2)sqrt(4x^2-1))`

or `f'(x)= 1/(sqrt(4x^4-x^2))`

In The Crucible, who called Elizabeth out and why?

According to Cheever, Abigail Williams made the claim that Elizabeth's spirit stuck needles into her (Abigail's) stomach. Cheever is then summoned to the Proctor house to question Elizabeth and look for evidence of this type of witchcraft. He finds a poppet (doll) with needles stuck in it. This is what Abigail claimed. She concluded that Elizabeth stuck needles in the doll and used her (voodoo) powers of witchcraft to inflict that violence on Abigail herself.

Of course, this is untrue. Abigail is pretending, and she had a role in using Mary Warren to plant the doll (poppet) in Elizabeth's home. As a result of Abigail's accusation and finding the poppet in her home, Cheever is forced to arrest Elizabeth.

Abigail accuses Elizabeth out of jealousy. She and John Proctor, Elizabeth's husband, had an affair, but John ended it. Abigail, still in love with John, did not want their relationship to end. When he abandons her, she takes her revenge upon Elizabeth. At this point, John Proctor's only hope is to convince Mary Warren to admit it was her poppet and the accusations of witchcraft are all false. John is outraged that his wife has been charged, but he must know his affair with Abigail indirectly contributed to his wife's arrest.

What is the title and author of the novel that was said to have started a “great big war”?

The book is Uncle Tom's Cabin, and the author is Harriet Beecher Stowe. Abraham Lincoln is said to have made this remark to her, and the exact quote is similar to "So you're the little lady who wrote the book that started this big war."

Uncle Tom's Cabin did indeed fan the flames of abolition in the years before the Civil War. Northerners were horrified that Southerners could be so cruel. They felt...

The book is Uncle Tom's Cabin, and the author is Harriet Beecher Stowe. Abraham Lincoln is said to have made this remark to her, and the exact quote is similar to "So you're the little lady who wrote the book that started this big war."

Uncle Tom's Cabin did indeed fan the flames of abolition in the years before the Civil War. Northerners were horrified that Southerners could be so cruel. They felt empathy for the slaves in the book. There were even stage productions of the book—during one stage production, someone pulled a gun and shot and killed one of the dogs that were chasing the "slaves" one the stage. Southerners claimed that the book was a collection of lies. Stowe never traveled to the South, so she could not write accurately on the subject. In some Southern areas the book was banned. Some Southern writers wrote about slaves who were happy to be slaves. These books did not have the staying power of Uncle Tom's Cabin. Stowe's novel helped to put a human face on the slavery issue in the 1850s and made people feel as though the nation had to decide whether or not it was to be free.

What are some important theories in International Relations?

Important theories in the field of international relations include the following:

• 
  Realism: this theory posits that in a dangerous world, states have one goal--self-preservation through enhancing their own power. Moral behavior is not rewarded, and cooperation between states is futile. Instead, states must look out for themselves. During the Cold War, the United States and the Soviet Union followed this policy. 


• 
  Liberalism: this theory developed in the 1970s in reaction to realism. This theory posits that military power can result in mutually assured destruction, so states can preserve themselves through cooperation and means other than military power. In an age of globalization, states are increasingly reliant on each other. In addition, rather than relying on military power, states can use economic power to achieve their objectives. While this theory recognizes that the world can be threatening, it advocates the use of forces other than military power to survive. Western countries used this type of response to force South Africa to eventually dissolve its policy of Apartheid (or racial segregation) in the 1980s and early 1990s.


• 
  Idealism: this theory posits that moral actions are the correct course of action in international relations. Idealism is often associated with U.S. President Woodrow Wilson and his hope to make the world safe for democracy through the League of Nations following World War I. 

Why do you think she counted the money thrice?

It is likely that Della counts the money three times simply out of sheer hope that the final count will yield a higher total. The first lines of the story tell us that Della has been saving up money to buy her husband, Jim, a Christmas present.

The text also tells us that it has been a challenging task for Della to save up enough money for a worthy present for Jim. Jim does not earn a...

It is likely that Della counts the money three times simply out of sheer hope that the final count will yield a higher total. The first lines of the story tell us that Della has been saving up money to buy her husband, Jim, a Christmas present.

The text also tells us that it has been a challenging task for Della to save up enough money for a worthy present for Jim. Jim does not earn a large income, and the household expenses are high. To save the $1.87, Della has to haggle with the grocer and the produce man, her efforts only saving her pennies at a time. For her part, Della is embarrassed at the memory of her haggling. She fears that she will be thought miserly for her efforts.

Della realizes that the $1.87 will never buy what she would consider a presentable gift for Jim. In her desperation, she counts the money three times ("thrice") to make absolutely sure that there is no mistaking the final total. In the end, Della sells her beautiful long hair for twenty dollars. With twenty-one dollars, she purchases a platinum fob chain for Jim's watch. Alas, Jim no longer has his watch: he sold it to pay for combs for Della's gorgeous hair.

T.S. Eliot states that "poetry is not a turning loose of emotion, but an escape from emotion; it is not the expression of personality, but an...

For T.S. Eliot and certainly other poets, writing poetry can indeed be an escape from emotion and personality.  For others, poetry is actually a way to process their emotions and demonstrate who they are. Let’s take a look at the poems of three very famous poets to test Eliot’s claim.

Thomas Hardy’s “The Darkling Thrush” is a great example of poetic escapism, if you will.  He develops a persona that is not his own and has this character present emotions designed to develop the mood and theme.  In stanza one, he uses the hyperbole that “all mankind” has sought to escape the haunting dreariness of life by staying close to hearth and home.  His message, then, is that all humans--not merely Hardy himself--have feelings of hopelessness. Certainly his word choice is designed to create shivery emotions in readers: the “spectre-grey” frost upon the “desolate” earth, the personification of “The Century’s corpse” upon the land, the metaphor of the sky as a “crypt” and the “wind his death-lament.” In the end we have this happy bird, symbolizing the determinedly hopeful person that the persona wishes he could be. Given the style of the poem, which is told by a fictitious persona, it is clear that Hardy is not presenting his own emotions and personality but developing a work of art to send a message to his audience.

However, very often poets do use their art form to process difficult emotions that are inextricably tied to their own personalities and lives. Sylvia Plath is a prime example of a poet who wrote herself onto the page. Her poem “Metaphors” is her attempt to deal with her own pregnancy through a series of gradually darkening metaphors that form a riddle.  At first she uses whimsical imagery to describe her swelling belly, such as “a melon strolling on two tendrils.” Her self-view quickly changes, however, as she feels like a means to an end, “a cow in calf.” Plath admitted that she felt the societal pressure on a woman to marry and have children yet experienced some resentment over what childbirth did to her body and feared that it would end her career. In “Metaphor,” she openly expresses her own emotions when she gives the defeatist analogy, “I’ve eaten a bag of green apples, / Boarded the train there’s no getting off.” She has eaten not just apples (perhaps alluding to Snow White and all the poisonous consequences she endured) but a whole bag of green ones.  Plath felt sick physically and sick at heart; her future was a riddle from that point forward. Clearly this is no invented persona.  Plath wrote the poem as way to process her own dark emotions concerning childbirth and motherhood.

One more demonstration of a poet putting his own emotions and personality into his poetry comes from Wilfred Owen in “Dulce Et Decorum Est.” Most of his poems stem from his experiences in the British Army during WWI.  He writes himself right into this piece as he uses a simile to depict how, “coughing like hags, we cursed through sludge.” These are raw emotions; the soldiers feel like old, worn-out crones, and they literally swear with frustration as even the mud seems bent on bringing them down. As Owen describes the graphic horror of watching a fellow soldier poisoned by gas warfare, we realize that this is likely a traumatic event he personally witnessed.  “He plunges at me, guttering, choking” is a vivid, haunting image.  We see Owen himself trudging behind the wagon they throw the dying man on.  Owen charges us with a sense of conviction when he says that we would not call war glorious if we could see this man’s “white eyes writhing in his face” or see “the blood / Come gargling from the froth-corrupted lungs.” The shocking imagery and the symbolism of the white eyes juxtaposed with the bloody mouth demonstrate the poet-soldier’s view that war makes victims of innocent young men. These are his emotions; this poem was his way of dealing with the nightmare of war. This is Wilfred Owen’s personality on the page.

What are the similarities between Flight to Canada and Josiah Henson's narrative on slavery?

Josiah Henson was an escaped slave who wrote The Life of Josiah Henson, Formerly a Slave, Now an Inhabitant of Canada, as Narrated by Himself (1849). Harriet Beecher Stowe is said to have based Uncle Tom in Uncle Tom's Cabin on Henson. One of the points that Henson makes is that slavery corrupts the masters. The slave owners' racism makes them oblivious to any value of the slave save their monetary value and what labor they can offer. Henson writes of slavery, "The natural tendency of slavery is, to convert the master into a tyrant, and the slave into the cringing, treacherous, false, and thieving victim of tyranny." Slavery corrupts the master so that he can no longer see the humanity of his slaves. After working for many years as a devoted and reliable slave, Henson is only valued for his labor. His master attempts to sell him, and Henson writes about his slave owner's family, "My merits, whatever they were, instead of exciting sympathy, or any feeling of attachment to me, seemed only to enhance my money value to them." In other words, his years of hard work are only valued for the financial worth they provide. His owner's family does not value his worth as a human.

In Flight to Canada, Reed satirizes the self-interested and racist perspective of slave owners. For example, Uncle Robin, a parody of a devoted slave, says to Swille, his owner, about Canada, "Canada. I do admit I have heard about the place from time to time, Mr. Swille, but I loves it here so much that...I would never think of leaving here" (page 19). Uncle Robin illustrates the racist way in which slave owners saw slaves merely as objects and dehumanized them as mere property while relying intensely on slaves for their survival. 

How does attention play a role in Embodied Cognition?

Embodied Cognition is the idea that our cognitions are affected by the body, not just the brain. In other words, the brain affects the body, and the brain also receives feedback from the body. According to Margaret Wilson (see the source below), attention plays a role in Embodied Cognition because the mind has limits with regard to attention and working memory. Therefore, the brain must relegate some functions of attention to the environment. For example,...

Embodied Cognition is the idea that our cognitions are affected by the body, not just the brain. In other words, the brain affects the body, and the brain also receives feedback from the body. According to Margaret Wilson (see the source below), attention plays a role in Embodied Cognition because the mind has limits with regard to attention and working memory. Therefore, the brain must relegate some functions of attention to the environment. For example, we can't pay attention to everything we must do and we can't store all this information in our long-term memory, so we store this information in calendars (both on paper and in electronic form). This allows us to reduce the load on our memory and attention and to pay attention to other elements of our environment. 

In addition, attention plays a role in Embodied Cognition because people have to be paying attention to their environment for the body and environment to provide feedback to the brain. In the experiment described by Wilson and Golonka (2013; see the source below), infants who watch a toy being hidden must then retrieve the toy. Infants' ability to retrieve the toy depends on their ability to pay attention; therefore, one's ability to pay attention affects one's ability to receive feedback from the environment.  

Wilson, Margaret (2002). "Six Views of Embodied Cognition." Psychonomic Bulletin & Review. 9 (4): 625–636. doi:10.3758/BF03196322.

Wilson, Andrew D. and Sabrina Golonka (2013). "Embodied Cognition is Not What you Think." Front Psychol. 2013; 4: 58. Published online 2013 Feb 12. doi: 10.3389/fpsyg.2013.00058.