What's wrong with this evaluation of $\lim _{x\to 2^-} \frac{|2x-x^2|}{x-2}$? 
Suppose we want to evaluate
$$\lim _{x\to 2^-} \frac{|2x-x^2|}{x-2}$$
Note that multiple answer choices may be correct.
I marked A and C as correct.
The websystem marked this incorrect.
I drew a graph of $-x^2 +2x$, parabola facing down, above the x-axis 0 < x < 2
So $|2x-x^2|  = -x^2 + 2x$ in the relevant interval.

There's no ambiguity here. The statement about the limit is correct, but the second statement is wrong simply because $|2x-x^2|=2x-x^2$ holds for $0<x<2$ and not $x<2$. There is no difference between $\textrm{for all }x<2$ and $\textrm{for }x<2$. The reason given is not given as a complement to the limit equation, but is given as an eternal statement which you need to check whether it's correct.
Hope this helps. Ask anything if not clear :)
