6.51. $\lim _{x \rightarrow 1} \frac{\sin 3 \pi x}{\sin 2 \pi x}$.
Solution.

$\lim _{x \rightarrow 1} \frac{\sin 3 \pi x}{\sin 2 \pi x}=(0 / 0)=\lim _{x \rightarrow 1} \frac{(\sin 3 \pi x)^{\prime}}{(\sin 2 \pi x)^{\prime}}=\lim _{x \rightarrow 1} \frac{3 \pi \cdot \cos 3 \pi x}{2 \pi \cdot \cos 2 \pi x}=-\frac{3}{2}$.

## INDETERMINACY OF THE FORM "0/0"