Find the following limit, if it exists.

Question

anonymous · Answer

$$ \lim_{x \rightarrow 2} \frac{ 3\left| x-2 \right| }{ x ^{2}-\left| x-2 \right|-4 }$$

anonymous · Answer

probably depends on what direction you are approaching 2 right?

anonymous · Answer

if $x<2$ then $|x-2|=2-x$ and if $x>2$ then it is $x-2$

anonymous · Answer

Maybe, I hadn't thought of that. Thank you!

anonymous · Answer

clear or no?

anonymous · Answer

yw
my first guess is there is no limit since the limit from the left and right will probably be different
i didn't try it though, but that is my guess

anonymous · Answer

There was an example we did in class that worked the same way, the x would change depending on wat direction you approached from and it results in different limits. I wasn't sure if that applied to every situaiton where absolute values were involved but now that i'm wokring it out it appears to be the case

anonymous · Answer

in general i would say yes, because the absolute value is a piecewise function

anonymous · Answer

Alright, I will make sure to check over this with my prof but what you said sounds good. Either way I appreciate you taking the time to respond, thank you!