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Question

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


A
1
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B
2
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C
1
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D
2
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Solution

The correct option is B $$-1$$

Consider the given equation.

$$\underset{x\to \pi }{\mathop{\lim }}\,\left( \dfrac{\sin x}{x-\pi } \right)$$

 

Apply L-hospital rule,

$$ \underset{x\to \pi }{\mathop{\lim }}\,\left( \dfrac{\cos x}{1-0} \right) $$

$$ \underset{x\to \pi }{\mathop{\lim }}\,\left( \cos x \right) $$

$$ =\cos \pi  $$

$$ =-1 $$

 

Hence, this is the answer.


Mathematics

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