Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

$\lim\limits_{x \rightarrow 0}\left(\frac{\sin \left(\pi \cos ^2 x\right)}{x^2}\right)$ equals

Options:

$-\pi$

$\pi$

$\frac{\pi}{2}$

1

Correct Answer:

$\pi$

Explanation:

$\lim\limits_{x \rightarrow 0} \frac{\sin (\pi(1-(\sin x)^2))}{x^2}$

$=\lim\limits_{x \rightarrow 0} \frac{\pi \sin \pi \sin ^2 x}{\pi \sin ^2 x} . \frac{\sin ^2 x}{x^2}$

$=\pi$

Hence (2) is the correct answer.