Question

The value of $\underset{x\to -\pi }{lim}\frac{x+\pi }{\sin x}$ is equal to

• A. $1$
• B. $-1$
• C. $\pi$
• D. Does not exist

Answer 1

The correct option is B $-1$

We have,

$\underset{x\to -\pi }{lim}\frac{x+\pi }{\sin x}$

This is $\frac{0}{0}$ form.

So, apply L-Hospital rule

$\underset{x\to -\pi }{lim}\frac{1+0}{\cos x}$

$\underset{x\to -\pi }{lim}\frac{1}{\cos x}$

$=\frac{1}{\cos (-\pi )}$

$=\frac{1}{\cos \left(\pi \right)}$

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

Hence, this is the answer.