# Thread: limits problem

1. ## limits problem

I just received my test back and was wondering how to find the steps of
lim as x-->2+ |x-2|/(2-x)

I got my answer by plugging values of x from the right side and got -1 but received 0 points. Anyone have any idea of how to solve it.

2. Originally Posted by sleepiiee
I just received my test back and was wondering how to find the steps of
lim as x-->2+ |x-2|/(2-x)

I got my answer by plugging values of x from the right side and got -1 but received 0 points. Anyone have any idea of how to solve it.
Well that is essentially what you're doing, but you can write it out more analytically.

The numerator is always positive because of the absolute value. What sign is the numerator as x starts off more than 2 and gets smaller and smaller? Well it's 2 minus a number slightly BIGGER than 2, so the sign is negative.

So now we know the sign of the limit is a positive divided by a negative, giving a negative.

As for the value itself, if you were to graph this for x > 2, it would be a horizontal line.... at? -1 like you said.

I don't know exactly what your teacher was looking for, but there's my informal reasoning. Does your teacher want you to use the definition of a limit? I doubt it.