Question

\[\lim_{x \to 0} \frac{x^2}{\sin x^2}\] 

Answer 1

\[\lim_{x \to 0} \left[ \frac{x^2}{\sin x^2} \right]\] 

\[\text{ When } x \to 0, \text{ then } x^2 \to 0 .\] 

Let \[\theta = x^2\] 

⇒ \[\lim_\theta \to 0 \left( \frac{\theta}{\sin\theta} \right)\]

= 1