131. Find $\lim _{x \rightarrow \infty} \frac{2 x^{3}-3 x^{2}+5 x+7}{3 x^{3}+4 x^{2}-x+2}$.
Solution. When $x \rightarrow \infty$, we have an indeterminate form of $\infty / \infty$. To resolve this indeterminacy, we divide the numerator and the denominator by $x^{3}$. Then we get

$$
\lim _{x \rightarrow \infty} \frac{2 x^{3}-3 x^{2}+5 x+7}{3 x^{3}+4 x^{2}-x+2}=\lim _{x \rightarrow \infty} \frac{2-\frac{3}{x}+\frac{5}{x^{2}}+\frac{7}{x^{3}}}{3+\frac{4}{x}-\frac{1}{x^{2}}+\frac{2}{x^{3}}}=\frac{2}{3}
$$

since $\frac{3}{x}, \frac{5}{x^{2}}, \frac{7}{x^{3}}, \frac{4}{x}, \frac{1}{x^{2}}, \frac{2}{x^{3}} \rightarrow 0$ as $x \rightarrow \infty$.

## 132-133. Find the limits: