Define w(x)={x2sin⁡ ⁣(1x),x≠0,0,x=0.w(x)=\begin{cases}x^{2}\sin\!\left(\dfrac{1}{x}\right), & x\neq 0,\\ 0, & x=0.\end{cases}…

Mathematics

Problem

Define w(x)={x2sin⁡ ⁣(1x),x≠0,0,x=0.w(x)=\begin{cases}x^{2}\sin\!\left(\dfrac{1}{x}\right), & x\neq 0,\\ 0, & x=0.\end{cases} Determine whether ww is differentiable at x=0x=0 by evaluating the limit that defines w′(0)w'(0). State your conclusion and give a brief justification.

Browse the problem library