# Another Limit Question- Limit of a function counterexample

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

## 1 Answer

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