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Thanks, sorry didn't read FAQ.

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closed as off topic by Fernando Muro, Emil Jeřábek, j.c., Andreas Blass, Alexandre Eremenko Nov 22 '12 at 15:05

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Looks like a HW problem in freshman calculus. –  Alexandre Eremenko Nov 22 '12 at 15:06

1 Answer 1

up vote -2 down vote accepted

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 $f/g\to 1$.

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It seems inconsistent to me to post an answer to a question and vote to close it. –  Gerry Myerson Nov 22 '12 at 21:47
    
Why inconsistent? I posted the answer so that you know the answer (you wanted to know this, did not you?). And voted to close because this question does not fit the site policies. What's inconsistent about this? –  Alexandre Eremenko Nov 25 '12 at 0:59

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