Answer
$$\frac{2}{7}$$
Work Step by Step
We have
$$
\lim _{x \rightarrow 0} \frac{\sin 2x}{\sin 7x} =\frac{0}{0}
$$
is an intermediate form, then we can apply L’Hôpital’s Rule as follows
$$
\lim _{x \rightarrow 0} \frac{\sin 2x}{\sin 7x} =
\lim _{x \rightarrow 0} \frac{2\cos 2x}{7\cos 7x} = \frac{2}{7}.
$$
