Question

let g(x)= (x^2+x-6)/abs(x-2) ... find lim g(x) as x--> 2+ (from the right) and as x--> 2- (from the left)

Answer 1

when we approach from right that is as x--->2+
abs(x-2) = (x-2)
and when we approach from left that is as x--->2-
abs(x-2)=-(x-2)

Answer 2

that should help

Answer 3

also x^2+x-6 = x^2+3x-2x-6 = x(x+3)-2(x+3)=(x-2)(x+3)

Answer 4

thank you! I got it! :)