Question

find the limit as x approaches zero for (2+x)^3 -8/x

Answer 1

undefined due to 0 in denominator

Answer 2

Actually, we have 0/0

lim[(2+x)^3 - 8]/x
= lim(3(2+x)^2)/1
= 3(4) = 12

Or, you can expand to get

(8 + 12x + 12x^2 + x^3 - 8)/x
= (12x + 12x^2 + x^3)/x
= 12 + 12x + x^2
= 12 as x->0