Limit question.
$$\lim_{x \rightarrow -2^{+}} (x+3) \frac{|x+2|}{x+2}$$

Question

anonymous · Answer

I'm sorry, but I don't understand. Can you explain your idea?

anonymous · Answer

Okay that way is just tooooo long lol. so you know that absolute values are going to make the lim at x=1 right? So; all you have to do is (-2+3)(1) and you will get 1 and the lim x-> -2 from the right will be 1 There is the answer

anonymous · Answer

is that one of your choices?

anonymous · Answer

I'm sorry!!! Actually I don't understand why absolute values are going to make the lim at x=1..

anonymous · Answer

The limit is a one-sided limit. So, you're asking to find the limit as you approach from the right. So, x  is greater than or equal to -2 as you get infinitely close to -2 from the right. So, the |x+2| = x+2. Then, you can cancel and evaluate your limit.

The same type of argument can be applied if you were to evaluate from the left side, but you'll get a different limit because your absolute value will simplify to something else.

anonymous · Answer

Oh! I got it, thanks!!!