# How do you find the limit of # (abs(x+2)-3)/(x-7 ) # as x approaches 7?

##### 2 Answers

#### Explanation:

and because the numerator is continuous

Note that this gives rise to a singularity **and** a 2 sided limit.

To test this in your head, mentally plug in, say,

So we say that:

The limit does not exist.

#### Explanation:

Simple substitution of

However, if

#lim_{x -> 7^-} frac{abs(x+2)-3}{x-7} = -oo#

Similarly, if

#lim_{x -> 7^+} frac{abs(x+2)-3}{x-7} = oo#