Question

evaluate lim x^3 -8 divided by x^2 -4 as x approaches 2

Answer 1

Go on:
wolframalpha dot com

When page be open in rectangle type:

limit ((x^3-8)/(x^2-4)) as x->2
and click option =

After few seconds when you see result click option: Show steps

Answer 2

At a 0/0 singularity such as this, you just take the ratio of derivatives:
(3x^2)/2x = (3/2)*x = 3

That is called L'Hopital's Rule.

Answer 3

(x-2)(x^2+2x+4)
=================
(x-2)(x+2)

(x^2+2x+4)
=================
(x+2)

when x = 2

(4+4+4)
=================
(2+2)

3