lim (absolute value (x))/(x) as x--(-2)

Question

lim (absolute value (x))/(x) as x-->(-2)

anonymous · Answer

Try direct substitution.

anonymous · Answer

attachment

anonymous · Answer

Here is some of my work. I get two different answers, (-1) and 1.

anonymous · Answer

BUt apparently the answer is only (-1). What is incorrect in what I did?

anonymous · Answer

|x| is always positive.

anonymous · Answer

-1 is the answer

anonymous · Answer

|x| = -x is never true.

anonymous · Answer

It's a positive divided by a negative, so the answer has to be negative.

helder_edwin · Answer

when $x\to-2+$ the variable $x$ is negative. so
$$ \large \lim_{x\to-2+}\frac{|x|}{x}=\lim_{x\to-2+}\frac{-x}{x} $$

anonymous · Answer

Ah, so I'm just plugging in (-2) directly into the absolute value to get positive 2 then. See, I was watching this video( http://www.youtube.com/watch?v=TUPkwGlrT8A), and this guy did the (-x) thing with absolute value of x. It's at about the 1:00 mark. Is he wrong the way he does that?

helder_edwin · Answer

the only difference with your problem and the u-tube video is that you have $x\to-2$, i.e., the variable approaches a negative value and the absolute u r given is not symetric with respect to -2.
in the video, the absolute value u see is symetric with respect to 1.

anonymous · Answer

I see. Ok, thanks for the help everyone.