MathDB

Miklos Schweitzer 1968_9

Source:

October 8, 2008

functionlimitreal analysisreal analysis unsolved

Problem Statement

Let

f(x)

be a real function such that \lim_{x \rightarrow \plus{}\infty} \frac{f(x)}{e^x}\equal{}1 and

|f''(x)|\leq c|f'(x)|

for all sufficiently large

x

. Prove that \lim_{x \rightarrow \plus{}\infty} \frac{f'(x)}{e^x}\equal{}1. P. Erdos