Question 5
A function $f$ is defined and differentiable on $[0,+\infty)$. For every $x\ge0$, it satisfies:
(a) $|f(x)|\le5$;
(b) $f(x)f'(x)\ge\sin x$.
Does $\lim_{x\to+\infty}f(x)$ exist?
(a) $|f(x)|\le5$;
(b) $f(x)f'(x)\ge\sin x$.
Does $\lim_{x\to+\infty}f(x)$ exist?