Question

$\displaystyle \lim_{x \to0} \frac{\sin\left(\pi\cos^{2}x\right)}{x^{2}} $ equals

• A. $ - \pi $
• B. $ \pi $
• C. $\pi/2 $
• D. 1

Answer 1

Answer: (B)

Consider
$\displaystyle\lim_{x \to0} \frac{\sin\left(\pi\cos^{2}x\right)}{x^{2}}$
$ =\displaystyle\lim_{x \to0} \frac{\sin\left(\pi - \pi\sin^{2} x\right)}{x^{2}}$
$ \left[ \because\sin \left(\pi- \theta\right) = \sin\theta\right]$
$ = \displaystyle\lim_{ x \to0} \frac{\sin\left(\pi\sin^{2}x\right)}{\pi\sin^{2}x} \times \frac{\pi\sin^{2}x}{x^{2}} = \pi $