MathDB

Differentiable function

Source: Vietnam NMO 1987 Problem 5

February 4, 2009

functiontrigonometrylimitintegrationalgebra unsolvedalgebra

Problem Statement

Let f : [0, \plus{}\infty) \to \mathbb R be a differentiable function. Suppose that

\left|f(x)\right| \le 5

and

f(x)f'(x) \ge \sin x

for all

x \ge 0

. Prove that there exists \lim_{x\to\plus{}\infty}f(x).