Question

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

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

Answer 1

Answer: (B)

Consider
$\underset{x\to 0}{\lim }\frac{\sin \left(\pi {\cos }^{2}x\right)}{x^2}$
$=\underset{x\to 0}{\lim }\frac{\sin \left(\pi -\pi {\sin }^{2}x\right)}{x^2}$
$\left[\because \sin \left(\pi -\theta \right)=\sin \theta \right]$
$=\underset{x\to 0}{\lim }\frac{\sin \left(\pi {\sin }^{2}x\right)}{\pi {\sin }^{2}x}\times \frac{\pi {\sin }^{2}x}{x^2}=\pi$