_ x 0 ( ^2 x ) x^2 equals - Vidyadip

MCQ

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

A
$-\pi$
✓
$\pi$
C
$\frac{\pi}{2}$
D
1

✓

Answer

Correct option: B.

$\pi$

(B)
$\lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^2 x\right)}{x^2}=\lim _{x \rightarrow 0} \frac{\sin \left(\pi-\pi \cos ^2 x\right)}{x^2}$
$=\lim _{x \rightarrow 0} \frac{\sin \left(\pi \sin ^2 x\right)}{\pi \sin ^2 x} \times \frac{\pi \sin ^2 x}{x^2}=\pi$

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