133. Find $\lim _{x \rightarrow \infty} \frac{4 x^{3}+x^{2}-2}{3 x^{2}+5 x-2}$.
Solution. Dividing the numerator and the denominator by $x^{3}$ and taking the limit, we get

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

since the numerator of the last fraction tends to a limit different from zero, while the denominator tends to zero.