# Rate of Convergence (1 Viewer)

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#### ductiletoaste

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

#### ductiletoaste

Can anyone give me any advice?

#### mathman

The description you gave of the professor's explanation is very confusing.

#### ductiletoaste

ur telling me. I have been lost and thats a not a description its a direct quote from one of his lectures! But for the sake of helping me figure this out lets forget the whole confusing explantion. how would u normally find the Rate of convergence of 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)?

#### mathman

Could you define "rate of convergence"?

#### ductiletoaste

no offense but if u don't know what rate of convergence is then u cant hope to answer this question.

#### mathman

I've been a mathematician all my life. I never heard that particular term used in an absolute sense, only relative to something else, like x3 -> 0 faster than x2 when x -> 0.

#### ductiletoaste

Well this was an example problem given to me by a Phd professor. So i can assure you there is nothing wrong with the question.

#### mathman

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))?
The first statement says that |F(h)-L| -> 0 at the same rate as G(h)->0.
The second statement means that |F(h)-L| -> 0 faster than G(h) -> 0.

Did you edit the statement after first posting?

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