Question

limita cand x tinde la -infinit din (eˣ-ax)/x ?

Answer 1

$L=lim_{x->-Inf}{\frac{e^{x}-ax}{x}}=lim_{x->-Inf}{\frac{x(\frac{e^{x}}{x}-a)}{x}}=lim_{x->-Inf}{\frac{e^{x}}{x}-a}=lim_{x->-Inf}{\frac{e^{x}}{x}}-a$
calculam separal limita obtinuta
$lim_{x->-Inf}{\frac{e^{x}}{x}}=<span>lim_{x->-Inf}{\frac{1}{e^{-x}*x}}=\frac{1}{e^{+Inf}*(-Inf)}=\frac{1}{-Inf}=0</span>$
Atunci avem
$L=0-a=-a$

Answer 2

Limita este imediata deoarece e la -infinit =0, iar -ax/x tinde la -a.