Answer
(a) $L=\lim _{\theta \rightarrow 0} \frac{14 \sin \theta}{\theta}$
(b) $L=14$.
Work Step by Step
Given $$ L=
\lim _{x \rightarrow 0} \frac{\sin 14x}{x}.
$$
(a) Putting $\theta =14x $, when $ x\to 0$ then $\theta \to 0$ . Hence, we have
$$ L=
\lim _{x \rightarrow 0} \frac{\sin 14x}{x}=\lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta/14}=\lim _{\theta \rightarrow 0} \frac{14 \sin \theta}{\theta}.
$$
(b) $$ L=
\lim _{\theta \rightarrow 0} \frac{14 \sin \theta}{\theta}=14 \lim _{\theta \rightarrow 0} \frac{ \sin \theta}{\theta}=14.
$$
Where we used the fact that $\lim _{\theta \rightarrow 0} \frac{ \sin \theta}{\theta}=1$.
