Question

limit ((x-2)/(abs(x)-2),x,2)

Answer 1

\[\lim_{x \to 2} {x-2 \over \left| x \right|-2}\]

Answer 2

hint: use |x|=x for when x>=0 (since 2>0)

Answer 3

when x is positive: the graph looks like a horizontal line with the point at x=2 missing .

Since the (x-2)/(abs(x)-2) = 1 on both sides of x=2 . the limit is 1