[tex] \lim_{x \to \infty} \frac{|x-2|}{x-2} [/tex] 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 [tex] \frac{-1(x-2)}{x-2} [/tex] 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 [tex] \frac{-1(x-2)}{x-2} [/tex] or -1
