Question

(3x |x-2|) / x-2
What is the limit as x approaches 2 from the left side?

Answer 1

while x < 2, -2 < 0, so, |x-2| = -(x-2)

So, you have the limit of

(3x(-(x-2)))/(x-2) = -3x
You can cancel the x-2 since x is not actually 2.

The limit is thus -6

The limit from the right, of course would be +6

See the graph at

http://www.wolframalpha.com/input/?i=%283x+|x-2|%29+%2F+%28x-2%29