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?

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