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I need to find an example of a function $f(x)$ , that satisfies: $ \lim _ {x\to 0} \frac{f(x)}{x^2} = 5 $ , but $\lim _ {x \to 0 } f(x) $ doesn't exist.

Does someone have an idea?

Thanks in advance !

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Such a function $f$ does not exist. Could you prove it? –  Did Nov 12 '12 at 16:45

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up vote 1 down vote accepted

Hint $\ $ Take the limit as $\rm\:x\to 0\:$ of $\rm\: f(x)\, =\, x^2 \dfrac{f(x)}{x^2}\ $ using the limit product rule.

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Thanks a lot !! there was indeed a mistake in the question's formulation –  joshua Nov 12 '12 at 17:12

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