Find a Function That Satisfies the Following Criteria

Question

Find a function $f$ satisfying both

1. $\lim_{x\to 0} f(x)=0$;
2. $\lim_{x\to 0} \frac{f(x)}{x}$ does not exist.

This one got me stumped (Sorry in advance for the bad formatting, I cant seem to get it)

Answer 1

Let $f(x)=|x|$.

Can you verify that this works?