Question

The value of $\underset{\theta \to 0}{lim}\frac{\sin \sqrt{\theta }}{\sqrt{\sin \theta }}$ is equal to

• A. $0$
• B. $1$
• C. $-1$
• D. none of these

Answer 1

The correct option is B $1$

$\underset{\theta \to 0}{lim}\frac{\sin \sqrt{\theta }}{\sqrt{\sin \theta }}$

$=\underset{\theta \to 0}{lim}\frac{\sqrt{\theta }\sin \sqrt{\theta }}{\sqrt{\theta }\sqrt{\sin \theta }}$

$=\underset{\theta \to 0}{lim}\frac{\sin \sqrt{\theta }}{\sqrt{\theta }}\times \underset{\theta \to 0}{lim}\sqrt{\frac{\theta }{\sin \theta }}$

$=1$....................$(\because {lim}_{\theta \to 0}\frac{\sin \theta }{\theta }=1)$