[tex]i)\text{Asimptota orizontala:}\\
\displaystyle\limit\lim_{x\to \infty} f(x)=\displaystyle\limit\lim_{x\to \infty} \dfrac{x^2-2}{x+1} =\infty \\
\text{Deci nu exista asimptote orizontale.}\\
\\
ii)\text{Asimpote verticale:}\\
\displaystyle\limit\lim_{x\searrow -1} f(x)= \displaystyle\limit\lim_{x\searrow -1} \dfrac{x^2-2}{x+1}= \dfrac{-1}{0^{+}}=\infty\\
y=-1 \text{ asimptota verticala.}\\
[/tex]
[tex]
iii)\text{Asimptote oblice:}\\
m=\displaystyle\limit\lim_{x\to \infty} \dfrac{f(x)}{x}=\displaystyle\limit\lim_{x\to \infty} \dfrac{x^2-2}{x^2+x}= 1 \Rightarrow m=1\\
n=\displaystyle\limit\lim_{x\to \infty}(f(x)-x)=\displaystyle\limit\lim_{x\to \infty} \left(\dfrac{x^2-2}{x+1}-x\right)=\displaystyle\limit\lim_{x\to \infty} \dfrac{-x-2}{x+1}=-1\Rightarrow \\ \Rightarrow n=-1\\
y=x-1\text{ asimptota oblica} [/tex]
