Chapter 2 - Limits - 2.6 Trigonometric Limits - Exercises - Page 77: 21

$1$

\begin{align*} \lim _{x \rightarrow 0} \frac{ x^2}{\sin^2 x}&=\lim _{x \rightarrow 0} \frac{x}{\sin x}\frac{x}{\sin x}\\ &=\lim _{x \rightarrow 0} \frac{x}{\sin x}\lim _{x \rightarrow 0}\frac{x}{\sin x}\\\ &=1. \end{align*}