Lim x-> 2+ (x + 3) times [(absolute value (x + 2)) / (x + 2)]?

Question

also, lim x-> 2- (x + 3) times [(absolute value (x + 2)) / (x + 2)]

Find the limits please! And explain how to solve them.

Answer 1

just graph the equation and look at what is happening in the graph as it approaches 2 from both sides.  

Answer 2

Both come out to 5. Just put 2 in for x.

(2+3)(abs(4)/4)) = 5*1 = 5

Now, if x were approaching -2, the problem would be considerably more interesting.