Question

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

Answer 1

$\underset{x\to 0}{\lim }\left[\frac{x^2}{\sin x^2}\right]$

$\mathrm{When}x\to 0,\mathrm{then}{x}^2\to 0.$

Let $\theta =x^2$

⇒ $\underset{\theta \to 0}{\lim }\left(\frac{\theta }{\sin \theta }\right)$

= 1