$f$ is bounded function defined around $x_0$. For every monotonic sequence $x_n \rightarrow x_0$, $f(x_n)$ is convergent.
all $f(x_n)$ sequences converge to the same limit when $x_n\rightarrow x_0$ is monotonic increasing func.
one sided limits of $f$ exist at $x_0$.
I think 1 is not correct so I am trying to find 2 monotonic sequences $x_n,y_n$ that converge to $x_0$ s.t $\lim f(x_n)$ Differ from $\lim f(y_n)$, but no success so far.
not sure about 2
I would appriciate any hint.