If $f$ is differentiable at $[a,+\infty$) and $\lim_{x\to\infty}(f(x)+f'(x))=c\in\mathbb{R}$. Prove that $lim_{x\to\infty}f(x)=c$.
If $\lim_{x\to\infty}(f(x)+f'(x))=L$ show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$