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

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

Define

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

Determine whether

w

is differentiable at

x=0

by evaluating the limit that defines

w'(0)

. State your conclusion and give a brief justification.