Let f(x) be a real function such that
\lim_{x \rightarrow \plus{}\infty} \frac{f(x)}{e^x}\equal{}1
and ∣f′′(x)∣≤c∣f′(x)∣ for all sufficiently large x. Prove that \lim_{x \rightarrow \plus{}\infty} \frac{f'(x)}{e^x}\equal{}1.
P. Erdos functionlimitreal analysisreal analysis unsolved