137. Find $\lim _{x \rightarrow \infty} \frac{3 x^{2}+5 x+1}{x^{2}-2}$.
Solution. Method I. Dividing the numerator and the denominator by $x^{2}$, we find

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

Method II. Let $x=1 / a$; then $a \rightarrow 0$ as $x \rightarrow \infty$. Therefore,

$$
\lim _{x \rightarrow \infty} \frac{3 x^{2}+5 x+1}{x^{2}-2}=\lim _{a \rightarrow 0} \frac{3 \cdot \frac{1}{a^{2}}+5 \cdot \frac{1}{a}+1}{\frac{1}{a^{2}}-2}=\lim _{a \rightarrow 0} \frac{3+5 a+a^{2}}{1-2 a^{2}}=3
$$

138-141. Find the limits: