Question

$\underset{x\to 0}{lim}\frac{|\sin x|}{x}$

• A. 1
• B. -1
• C. does not exist
• D. none of these

Answer 1

The correct option is C does not exist

$LHL={lim}_{x\to 0^{-}}\frac{\left|\sin x\right|}{x}$

$={lim}_{x\to 0^{-}}\frac{-\sin x}{x}=-1$

$RHL={lim}_{x\to 0^{+}}\frac{\left|\sin x\right|}{x}$

$={lim}_{x\to 0^{+}}\frac{\sin x}{x}=1$

$\therefore LHL\ne RHL$

Hence the limit does not exist.