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$\begingroup$

$\lim_{x\to 0^+} \frac{1}{x}=\infty$

But with l'Hospital's Rule

$\lim_{x\to 0^+} \frac{1}{x}=\lim_{x\to 0^+} \frac{0}{1}=0$

So where's my naive mistake?

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    l'Hopital's rule doesn't apply here.2012-08-23

2 Answers 2

8

I believe l'Hopital's rule works only for indeterminate forms.

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    Ah, of course. How silly of me. :) Thanks!2012-08-23
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l'Hospital's Rule works on limits of the form "$\frac{0}{0}$" and "$\frac{\infty}{\infty}$" so you can not use it to evaluate your limit.

You can find the complete list of conditions you need to verify befote using l'Hospital's Rule here

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    @RobertIsrael Yes, my mistake. Thanks!2012-08-24