Let $f$ be a continous differentiable function on $\mathbb R$. Suppose that $$L = \lim_{x \to \infty} ( f(x) + f'(x) )$$ exists. If $ 0 < L < \infty$, then which of the following statments is / are true ?
if $\lim_{ x \to \infty} f'(x)$ exists, then it is $0$.
if $\lim_{ x \to \infty} f(x)$ exists, then it is L.
if $\lim_{ x \to \infty} f'(x)$ exists, then $ \lim _{x \to \infty} f(x) = 0$ .
if $\lim_{ x \to \infty} f(x)$ exists, then $ \lim _{x \to \infty} f'(x) = L$
Any help would be appreciated. Thank you
