Question

Evaluate: $\underset{x\to 0}{lim}\frac{x^2}{2{\sin }^2\frac{x}{2}}$

Answer 1

$\underset{x\to 0}{lim}\frac{x^2}{2{\sin }^2\frac{x}{2}}$

$[\therefore \underset{\theta \to 0}{lim}\sin \theta =\theta ]$

$\Rightarrow \underset{x\to 0}{lim}\frac{x^2}{2{\left(\frac{x}{2}\right)}^2}$

$=2$