# Limits to infinity of functions ratio [closed]

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Looks like a HW problem in freshman calculus. –  Alexandre Eremenko Nov 22 '12 at 15:06
No. Take $f(x)=\exp(-1/x),\; g(x)=\exp(-1/x^2)$. Then $\lim(f'/f)/(g'/g)=\lim(\log f)'/(\log g)'=\infty$, but $f/g\to 1$.