Alright, the question is:
By identifying each of the following limits as a derivative, find the value of the limit.

lim h->0 (((27+h)^1/3)-3)/h

I see how this fits into the definition of a derivative

f'(a) = lim h->0 (f(a+h) - f(a))/h, but I don't understand how I'm supposed to use this information to evaluate the limit.

I see that the f(x) = cuberoot (x) and a=27 so f(a) = 3

Any instruction would be highly appreciated. I'm taking an online calculus course so can only correspond with my tutor via email and am finding her to be extremely unhelpful.

Thanks!

2. Originally Posted by shelter22
I see that the f(x) = cuberoot (x) and a=27 so f(a) = 3
You almost done!
So the limit = $f'(27)$.
Find the derivative of $f$ and substitute $x=27$ to get the value of the limit.

Spoiler:

Your answer should be $\frac{1}{27}$