Question

$\underset{x\to 0}{lim}\left[\frac{-x}{\sin x}\right]=$

Answer 1

Consider the given function

$f\left(x\right)=\underset{x\to 0}{lim}\left[\frac{-x}{\sin x}\right]$

$=\underset{x\to 0}{lim}\left[\frac{-1}{\frac{\sin x}{x}}\right]$

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

$=\frac{-1}{1}=1$

hence, this is the answer.