(1)
\begin{align}
\lim_{x \to 0} \frac{1 – \cos 2 x}{x^2}
\end{align}
(2)
\begin{align}
\lim_{x \to 0} \frac{\sin 3 x}{x}
\end{align}
(3)
\begin{align}
\lim_{x \to \pi} \frac{\sin x}{x – \pi}
\end{align}
(1)
\begin{align}
\lim_{x \to 0}\frac{1 – \cos 2 x}{x^2} &= \lim_{x \to 0}\frac{2 \sin 2 x}{2 x} \\
&= 2
\end{align}
(2)
\begin{align}
\lim_{x \to 0} \frac{\sin 3 x}{x} &= 3 \lim_{x \to 0} \frac{\sin 3 x}{3 x} \\
&= 3
\end{align}
(3)
\begin{align}
\lim_{x \to \pi} \frac{\sin x}{x – \pi} &= \lim_{x \to \pi}\frac{\cos x}{1} \\
&= – 1
\end{align}
