Question

$\underset{x\to 0}{\lim }$ $\frac{|sinx|}{x}$ is

• A. $1$
• B. $-1$
• C. Does not exist
• D. None of these

Answer 1

Answer: (C)

We have, $\underset{x\to 0}{\lim }$ $\frac{|sinx|}{x}$
$L.H.L$ $=\underset{x\to 0^{-}}{\lim }$ $\frac{|sinx|}{x}$
$=\underset{h\to 0}{\lim }$ $-\left(\frac{sinh}{h}\right)$
$=\left(-1\right)\times 1=-1$
$R.H.L.$ $=\underset{x\to 0^{+}}{\lim }$ $\frac{|sinx|}{x}$
$=\underset{h\to 0}{\lim }$ $\frac{sinh}{h}=1$
Since $L.H.L.\ne R.H.L.$
$\therefore$ Limit does not exist