# Evaluate limit

1. Sep 22, 2014

### Aviegaille

1. The problem statement, all variables and given/known data
Evaluate lim h->0 ((8+h)^⅓ -2)/h.

2. Relevant equations
Hint: Let 8+h=x^3

3. The attempt at a solution
I've uploaded a picture of my calculation. But I am not sure if that is the final answer or is there a following step to get the answer.

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2. Sep 22, 2014

### Dick

Why do you think that as h->0 with x^3=8+h that x->(-3)? And why do you think that (x^3)^(1/3)=x^3?

3. Sep 22, 2014

### Ray Vickson

Please do not post thumbnails; they cannot be viewed on some media! Just type out things directly.

4. Sep 23, 2014

### HallsofIvy

Staff Emeritus
I don't know exactly which of many possible methods you are expected to use here, but did you notice that this limit is precisely that defining the derivative of f(x) at x= 8, with $f(x)= x^{2/3}$?