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