Question

$\underset{x\to 0}{lim}\left(\frac{x-\sin x}{x}\right)\sin \left(\frac{1}{x}\right)$.

Answer 1

$\underset{x\to 0}{lim}(1-\frac{\sin x}{x})\sin \frac{1}{x}$

Indeterminate as $\sin \frac{1}{x}$ cannot be determined as it oscillates between $0$ and $1$.