Question

The function f has derivatives of all orders. Let g be the function defined by

Answer 1

\[f(x) = (\cos x - 1)/ x^2 for x \neq 0 and -1/2 for x = 0\]

Answer 2

Write the first three nonzero terms and the general term of the Taylor series for f about x = 0.

Answer 3

Write the fifth degree Taylor polynomial for g about x = 0.