Define f(x)= cases x^ 2 ! ( 1 x ), & x 0, 0, & x=0

MATHEMATICS · Subjective · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

Define

f(x)=\begin{cases}x^{2}\sin\!\left(\dfrac{1}{x}\right), & x\ne 0,\\ 0, & x=0.\end{cases}

Determine whether

f'(0)

exists and, if so, give its value.