help with Maclaurin series for f(x): find f'(0), f"(0), and

[bobbob_924]

8. The Maclaurin series for f (x) is given by
2 3
2 2 2 2 ... 2 1
2! 3! !
k
x x xk
k
+ + + + ? (12 points)
a. Find f '(0), f "(0) and f 7 (0)
b. For what values of x does the given series converge? Explain your reasoning.
c. Let g(x) = xf (x) . Write the Maclaurin series for g(x), showing the first three nonzero
terms and the general term.
d. Write g(x) in terms of a familiar function without using series. Then, write f (x) in
terms of the same familiar function.

 

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