Question

Calculati limita:

$\lim_{x \to -\infty} x * e^{x}$

Answer 1

[tex]\lim_{x\rightarrow-\infty}(xe^x)=\lim_{x\rightarrow-\infty}\frac{x}{e^{-x}}=\lim_{x\rightarrow-\infty}\frac{x'}{(e^{-x})'}=\\ =\lim_{x\rightarrow-\infty}\frac{1}{-e^{-x}}=\frac{1}{-\infty}=0[/tex]