$f(x)$ is differentiable on $\mathbb{R}$, If $\lim_{x \to \infty}f'(x)=a$,then show $\lim_{x \to \infty}(f(x+1) - f(x))=a$
If $\lim_{x\to\infty} f'(x) = L$, prove that $\lim_{x\to\infty} f(x+c)-f(x) = cL$ and $\lim_{x\to\infty} f(x)/x=L$