## Calculus (3rd Edition)

$$2.5$$
We need to find $$\lim _{\theta \rightarrow 0} \frac{\sin 5 \theta}{\sin 2 \theta}$$ Consider the function $$f(\theta)= \frac{\sin 5 \theta}{\sin 2 \theta}$$ From the following figure, we can observe that \begin{align*} \lim _{\theta \rightarrow 0^+} f( \theta)&=2.5\\ \lim _{\theta \rightarrow 0^-} f( \theta)&=2.5 \end{align*} Since the left and right limits equal each other, we can say that $$\lim _{\theta \rightarrow 0} \frac{\sin 5 \theta}{\sin 2 \theta}=2.5$$