Question

determine the following limit: limit as x approaches 2 of (x^2-8)/(x-2)

Answer 1

Don't know if it is x^3-8 or x^2-8, please check.
If it is x^3-8, here's the solution
Lim (x^3-8)/(x-2)
x->2
=
Lim (x-2)(x^2+2x+4)/(x-2)
x->2
Since x does not equal 2, we can cancel the common factors (x-2)
So the limit is (x^2+2x+4)=12

If the expression is x^2-8, then the limit is infinity, since the numerator is finite, and the denominator is zero.