limit (x->4+) of ((x^2)-x)/(x-4)^2?

Answer 1

Let x be 4 + h for h>0

(x^2 - x)/(x - 4) = [(4 + h)^2 - 4 - h]/h^2 =
= (16 + 8h + h^2 - 4 - h)/h^2 = (12 + 7h + h^2)/h^2

The denominator goes to zero and always positive as h->0
While The numerator is greater than 12.

Thus, the limit is +inf.