Question

lim of 2-|x|/2+x as you approach -2

Answer 1

For \(x<0\) (that includes \(x=-2\)), you have \(|x|=-x\).
\[\lim_{x\to-2}\frac{2-|x|}{2+x}=\lim_{x\to-2}\frac{2-(-x)}{2+x}\]

Answer 2

isnt there more to it as well?

Answer 3

Simplify it. \(2-(-x)=2+x\), so you have \(\dfrac{2+x}{2+x}=\cdots\).

Answer 4

its one but since its a absolute value problem dont you have to evaluate it from both sides?

Answer 5

No. The function is perfectly continuous for all values of \(x\) other than -2. The limit takes advantage of this fact; we're only *approaching* 2, and not actually *touching* it.