How do I show $\lim_{x\to\infty}f(x) = \lim_{x\to\infty} f '(x)=0$ if $\lim_{x\to\infty}f '(x)^2 + f(x)^3 = 0$?
How prove that $\lim\limits_{x\to+\infty}f(x)=\lim\limits_{x\to+\infty}f'(x)=0$ if $\lim\limits_{x\to+\infty}([f'(x)]^2+f^3(x))=0$?