The importance of plugging in -2 first is that you can determine if you're dealing with an undetermined form or not, in this case you see you get the undetermined form: .
Calculating:
Now plug in -2 again, so what's the limit?
Thanks Siron for pointing out where I went wrong in my working. Here is what I got:
I want to be clear on this and correct me if I am wrong: if I get an undetermined value when I plug in the value (e.g. -2), then I have to calculate the limit the long way, which is what we just did. Otherwise, if I don't get an undertermined value, then the answer is the limit?
Where did the x^2 suddenly appear from? If what you now post is what you really want then plugging -2 in for x won't work because what you get is indeterminate.
You will either have to use L'Hopital's rule or the substitution u=x+2 and consider the resulting limit as u goes to zero
CB