Example 4. $\quad f(x)=\frac{x^{3}+3 x^{2}}{x^{2}-2}$.
Solution.

$$
\begin{gathered}
k=\lim _{x \rightarrow \infty} \frac{f(x)}{x}=\lim _{x \rightarrow \infty} \frac{x^{3}+3 x^{2}-1}{x\left(x^{2}-2\right)}=1 \\
b=\lim _{x \rightarrow \infty}(f(x)-k x)=\lim _{x \rightarrow \infty} \frac{3 x^{2}+2 x-1}{x^{2}-2}=3
\end{gathered}
$$

$y=x+3-$ the oblique asymptote.