Question

Asimptota spre minus infinit: f:R→R, f(x)=e^x+π^x

Answer 1

$\ Asimptota orizontala: \\ \\ \underset{x\rightarrow -\infty}{lim} e^x+\pi^x = e^{-\infty}+\pi^{-\infty} = \dfrac{1}{e^{\infty}} + \dfrac{1}{\pi^{\infty}} = \dfrac{1}{\infty} + \dfrac{1}{\infty} = 0 +0 \Rightarrow \\ \\ \Rightarrow y = 0, asimptota orizontala spre -\infty$

Asimptota oblica nu mai cautam fiindca am gasit deja asimptota orizontala, iar asimptota verticala nu cautam fiindca nu avem capete de intervale in domeniul de definitie.