Ok i have a question im have been stuck on for a while.

$\displaystyle g(x) = f(x)^(1/3) and f(x)^(1/3)= (e^x-cos(x)-x-x^2)^(1/3)$

non MATH version

g(x) = f(x)^(1/3) and f(x)^(1/3) = (e^x-cos(x)-x-x^2)^(1/3)

What is the rate of convergence for lim x->0 of g(x)?

Now to make it easier i took the taylor poly of the crazy function to degree 3. Which is (x^3)/6

The part im confused about is what our prof told us in class.....

lim h->0 of G(h) = 0, and lim h->0 of F(h) = L

We say that F(h) converges to L with a Rate of Convergence O(G(h)).

So what is the rate of convergence? and what is o(G(h))?

Thank you for any direction you can provide!