Find the n'th Taylor Polynomial centered at c

Taylor series is an example of infinite series derived from the expansion of about a single point. It is represented by infinite sum of  centered at  The general formula for Taylor series is:

or

 To evaluate the given function , we may express it in terms of fractional exponent. The function becomes:

.

Apply the definition of the Taylor series by listing the up to

 We determine each derivative using Power Rule for differentiation: .

          

         

         

         

          

          

         

Plug-in , we get:

         

         

         

         

         

         

         

Applying the formula for Taylor series centered at , we get:

   

   

   

   

   

   

The Taylor polynomial of degree  for the given function  centered at   will be: