why is this -infinity

Question

anonymous · Answer

(x+7)/(x^2-4)
limit approaches 2 negatively 
between -2 and 2 the denominator is negative but once it passes -2 it becomes +infinity so shouldn't it be +infinity instead of -infinity?

nicks · Answer

If you haven't already, graph the equation on your graphing calculator.  As you'll notice, if the limit is appoaching -2 from the left, then the answer will be positive infinity.  However, if the limit is approaching -2 from right, then the answer will be -infinity.

anonymous · Answer

so then instead of looking at the direction of y, I would look at the direction of x?

nicks · Answer

Does the limit in the problem look something like this? $$\lim_{n \rightarrow -2^+}$$

anonymous · Answer

$$g(x)=x+7/x ^{2}-4$$
$$\lim_{x \rightarrow 2^-} g(x)$$

nicks · Answer

All right, see how there is a "-" sign above the 2?  The negative sign means that the limit is approaching 2 from the left side.  If there was a "+" sign above the 2, then the limit would be apporaching 2 from the right side.  So, yes, it's how you look at from the direction of x.

anonymous · Answer

Alright, I getting to understand it, thanks!!

nicks · Answer

No problem, I'm glad I could help.