Finding a function $f(x)$ such that $\lim _ {x\to 0} \frac{f(x)}{x^2} = 5 $ , but $\lim _ {x \to 0 } f(x) $ doesn't exist

Question

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

Does someone have an idea?

Answer 1

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.