Is it necessary that if $\lim_{x \to \infty } f(x) + f'(x) = L$ , where $L$ is finite then $\lim_{x\to\infty}f(x)= L$ and $\lim_{x\to\infty}f'(x)=0$
If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L<\infty$, does $\lim\limits_{x\rightarrow\infty} f(x) $ exist?