Question

Evaluate :
$\underset{x\to 0}{lim}{x}^2\sin \left(\frac{1}{x}\right)$

Answer 1

We have

$\underset{x\to 0}{lim}{x}^2\sin \left(\frac{1}{x}\right)=0$

$\because \underset{x\to 0}{lim}{x}^2=0\sin \left(\frac{1}{x}\right)=0$ oscillates between $-1$ and $1$.

Hence, this is the answer.