Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

$\lim\limits_{x \rightarrow 0} \frac{\sqrt{\frac{1}{2}(1-\cos 2 x)}}{x}=$

Options:

1

-1

0

none of these

Correct Answer:

none of these

Explanation:

Given limit is $\lim\limits_{X \rightarrow 0} \frac{|\sin x|}{x}$

$\lim\limits_{X \rightarrow 0^{+}} \frac{|\sin x|}{x}=1$  and  $\lim\limits_{X \rightarrow 0^{-}} \frac{-\sin x}{x}=-1$

Hence (4) is the correct answer.