Mathematics

Problem

Consider the power series

f(x)=\displaystyle \sum_{n=0}^{\infty}\frac{x^{2n+1}}{2n+1}

, which converges for

|x|<1

. Using only the first three nonzero terms of

f'(x)

, which of the following is the best approximation of

f'(0.2)

? a)

1.0480

0.9615

1.0416

1.0400