I am in a dire need for you to answer this Limits question from Calculus. I would greatly appreciate anybody's constructive help ~ I would be really grateful.

Use lim (h -> 0) for (f(x+h) - f(x))/(h)

to solve the function:

f(x) = x ^ (2/3)

I would be soooo incredibly happy if you can answer this question! Thanks.

~ Riddhi.

use the following binomial expansion:

(x+h)^n = x^n + (x^(n-1))*n*h + (x^(n-2))*(n(n-1)/2!)*h^2 + ....

note that the above expansion holds true even if n is a fraction!

Solve the function for WHAT? For values where f(x) = 0? For a simplified version?

If you're looking for a root, x = 0 is the only root.

If you're looking for a different representation, then the answer given before me does work. Beware, though, that this representation goes on infinitely.