Voi folosi criteriul cleștelui.
[tex]-1 \leq \cos x\leq 1\Big|+x \\ \\ x-1\leq x+\cos x\leq x+1 \\ \\ \lim\limits_{x\to -\infty}(x-1)\leq \lim\limits_{x\to -\infty}(x+\cos x)\leq \lim\limits_{x\to -\infty}(x+1) \\ \\ -\infty \leq \lim\limits_{x\to -\infty}(x+\cos x)\leq -\infty \\ \text{}\,\,\,\,\quad\quad\searrow\quad\quad\quad\quad\quad\quad\swarrow\\\\ \Rightarrow \lim\limits_{x\to -\infty}(x+\cos x) = -\infty[/tex]
