Problem 80AE

Nonconvergence to f Consider the function

a. Use the definition of the derivative to show that f'(0) = 0.

b. Assume the fact that f(k)(0) = 0, for k = 1, 2, 3,.... (You can write a proof using the definition of the derivative.) Write the Taylor series for f centered at 0.

c. Explain why the Taylor series for f does not converge to f for x ≠ 0.

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