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This is an exercise in Stewart's Calculus:

If $\displaystyle\lim_{x \rightarrow 1} \frac{f(x)}{x^{2}} = 5$

Find: $\displaystyle\lim_{x \rightarrow 0} f(x)$

I can't figure this out. From my view, you can't tell anything about $f(x)$ when $x$ approaches zero, since the exercise only gives information about $x \to 1$. Any help?

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closed as too localized by Qiaochu Yuan Jun 3 '11 at 22:09

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Of course you can't say anything about this limit. This is a typo or there's some context around this exercise that you're missing. Consider $f(x)=5x^2$ and $f(x)=5x^2+x-1$. –  Alon Amit Apr 23 '11 at 1:16
You are absolutely right. I happen to have a recent (free) copy of Stewart, edition 7E. Problem 58, Section 2.3, has something that looks in part like what you wrote, except that it says "if $\lim_{x\to 0}f(x)/x^2=5$." So probably the typo has been caught and fixed. –  André Nicolas Apr 23 '11 at 1:28
@user6312: Ah! Thank you very much. Now it's easy! –  Pedro Apr 23 '11 at 1:34
Problem 56 here –  Henry Apr 23 '11 at 11:42

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