Ecuatia asimptotei este y=mx+n.
[tex]m=\displaystyle \lim_{x \to \infty} \frac{f(x)}{x} =\lim_{x \to \infty} \frac{x+e^{-x}}{x} =\ \ teorema \ l'hospital\\
=\lim_{x \to \infty} \frac{1+e^{-x}\cdot (-1)}{1}=\lim_{x \to \infty}(1- \frac{1}{e^x} )=1[/tex]
[tex]n=\displaystyle\lim_{x \to \infty}[f(x)-mx]=\lim_{x \to \infty}( x+e^{-x}-x)=\lim_{x \to \infty}e^{-x}=\\
=\lim_{x \to \infty} \frac{1}{e^x} =0[/tex]
In concluzie, ecuatia asimptotei oblice catre infinit este y=x.
