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quasar987

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**[SOLVED] Puzzled by this application of L'Hospital's rule**

## Homework Statement

In an example in my textbook, they define a function f on the real line by f(0)=0 and f(x)=exp(-1/x^2) otherwise.

They then say that we can evaluate f'(0) by L'Hospital's rule, and they write

[tex]f'(0)=\lim_{x\rightarrow 0}\frac{f(x)-f(0)}{x-0}=\lim_{x\rightarrow 0}\frac{e^{-1/x^2}}{x}=0[/tex]

How did they get that?? It seems if I apply L'Hospital, I get

[tex]\lim_{x\rightarrow 0}\frac{e^{-1/x^2}}{x}=\lim_{x\rightarrow 0}\frac{-2x^{-3}e^{-1/x^2}}{1}=\lim_{x\rightarrow 0}\frac{-2e^{-1/x^2}}{x^{3}}[/tex]

and thus I'm not more advanced!