pouvais vous m'aider a trouver la limite de:x-e^(-x) en +inf et - inf merci!!!!!

[tex]x-e^{-x} = x(1- \frac{e^{-x}}{x})\\\\ \lim_{x \to -\infty} (x) = -\infty \ \\ \lim_{x \to -\infty} (1)=1 \\lim_{x\to -\infty} ( \frac{e^x}{x})= 0 \\\lim_{x \to -\infty} (1- \frac{e^{-x}}{x})=1\\\\ \boxed{ \lim_{x \to -\infty} (x-e^{-x} ) = -\infty}\\\\ \lim_{x \to \infty} (x) = \infty \ \\ \lim_{x \to \infty} (1)=1 \\lim_{x\to \infty} ( \frac{e^x}{x})= \infty \\ \lim_{x \to \infty} (1- \frac{e^{-x}}{x})=\infty \\\\ \boxed{ \lim_{x \to \infty} (x-e^{-x} ) = \infty}[/tex]