009C Sample Final 3, Problem 5

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Consider the function

(a) Find a formula for the  th derivative    of    and then find  

(b) Find the Taylor series for    at    i.e. write    in the form

Foundations:  
The Taylor polynomial of     at     is

        where


Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  


Final Answer:  
   (a)
   (b)

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