Find an example (Limits)
I was asked about this problem
Find a function $f:\mathbb{R}\rightarrow\mathbb{R}$ such as the limit as
$x\to0$ of $f$ doesn't exist, and $\lim\limits_{x\to0}f(x)\cdot f(2x) = 0$
I think is really interesting and I would like to know what will be the
idea to came out with a solution.
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