Question

What is the limit of the absolute value of (x-2) divided by (x-2) as x approaches 2-

Answer 1

`\lim_(x \to \infty) (|x-2|)/(x-2)`
as approaches 2-
that '-' after the 2 means as it approaches from the left
ok
from the left, it is like from 1 to 2
as it approaches from the left, it is
`(-1(x-2))/(x-2)`
it is negative since when the value of x is smaller than 2, the value of x-2 is negative so then the absolute value is making it positive, to do that, we multiply it by -1
therefor

`(-1(x-2))/(x-2)` or -1

it approaches -1