Question

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

• A. $1$
• B. $2$
• C. $-1$
• D. $-2$

Answer 1

Answer: (C)

$-1$

Consider the given equation.

${lim}_{x\to \pi }\left(\frac{\sin x}{x-\pi }\right)$

Apply L-hospital rule,

${lim}_{x\to \pi }\left(\frac{\cos x}{1-0}\right)$

${lim}_{x\to \pi }\left(\cos x\right)$

$=\cos \pi$

$=-1$

Hence, this is the answer.