Question

What is $\underset{x\to 0}{lim}\frac{x}{\sqrt{1-\text{cosec x}}}$ equal to ?

• A. $\sqrt{2}$
• B. $-\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. Limit does not exist

Answer 1

The correct option is D Limit does not exist

as $x\to 0$, $\csc x\to \infty$ and $1-\csc x\to -\infty$

and hence, the value of $\sqrt{1-\csc x}$ is undefined and the limit does not exist.