Evaluate the limit as h approaches zero of

Question

(the cubed root of 8-h)-2/h.
Can also be written ((8-h)^1/3)-2)/h

Answer 1

let (8-h)^(1/3) = x
cube both sides
8-h = x^3
h = 8-x^3
as h--->0 , x ----> 2

so we write our limit as

lim (x - 2)/(8 - x^3) as x --> 2
= lim (x-2)/((x-2)(x^2 + 2x + 4) as x--2
= lim 1/(x^2 + 2x + 4)
= 1/(4+4+4) = 1/12