# I don't know how to compute this $\lim _{x\to \infty }\left(\left(1-\left|x\right|\right)e^{\frac{1}{2x+2}}\right)$?

Good evening to everyone, the limit is $\lim\limits _{x\to \infty }\left(\left(1-\left|x\right|\right)e^{\frac{1}{2x+2}}\right)$ and I don't know how to compute it I tried the limit substitution, the $e^{\ln x}$ technique and I tried to transform this case of $0\cdot \infty$ in a case of $\frac{\infty }{\infty }$ or $\frac{0}{0}$ but I don't know how. Thanks for any possible answers.

$\lim_\limits{x\to \infty }\left(\left(1-\left|x\right|\right)e^{\frac{1}{2x+2}}\right)=\lim_\limits{x\to \infty }\left(1-\left|x\right|\right)\lim_\limits{x\to \infty }e^{\frac{1}{2x+2}}\\ \lim_\limits{x\to \infty }e^{\frac{1}{2x+2}} = 1\\ \lim_\limits{x\to \infty }\left(1-\left|x\right|\right) = -\infty$

• Yeah, thanks. I didn't observe that. xD Jun 15 '16 at 19:57