Evaluating a Limit: Examining lim h->0 ((8+h)^⅓ -2)/h

[Aviegaille]

Homework Statement

Evaluate lim h->0 ((8+h)^⅓ -2)/h.

Homework Equations

Hint: Let 8+h=x^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.

 

[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?

 

[Ray Vickson]

Homework Statement

Evaluate lim h->0 ((8+h)^⅓ -2)/h.

Homework Equations

Hint: Let 8+h=x^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.

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

 

[HallsofIvy]

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}?