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Math Help - linear and quadratic convergence

  1. #16
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    Re: Simple minds...

    Quote Originally Posted by marijakopljar View Post
    Me again! Please, how do we get F(1) -F(0) = 2/3 which is right, but 1 to high power 0.5 is still 1!
    By definition of exponentiation, 1^{0.5}=1^{1/2}=\sqrt{1}, which is 1.

    Quote Originally Posted by marijakopljar View Post
    How do we get the derivative f(x) = 2/3(x) to high power 3/2?
    What exactly is f(x)? Do you mean that the derivative of f(x) is \frac{2}{3}x^{2/3}, or do you want to say that f(x)=\frac{2}{3}x^{2/3} is a derivative of something else? My guess is that f(x)=\sqrt{x}=x^{1/2} and its antiderivative F(x)=\frac{2}{3}x^{3/2} (plus a constant). This is so because \left(\frac{2}{3}x^{3/2}\right)'=x^{1/2} according to the power rule.

    In plain text, you can write x^(2/3) to mean x^{2/3}. Note the parentheses; x^2/3 means \frac{x^2}{3}.
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  2. #17
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    Re: linear and quadratic convergence

    Sorry, antiderivative!
    How do we get that antiderivative frm x2 = 1/3 x3???
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  3. #18
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    Re: linear and quadratic convergence

    Quote Originally Posted by marijakopljar View Post
    How do we get that antiderivative frm x2 = 1/3 x3???
    Quote Originally Posted by emakarov View Post
    This is so because \left(\frac{2}{3}x^{3/2}\right)'=x^{1/2} according to the power rule.
    Edit: Sorry, this is obviously the antiderivative of a different function, but the idea is the same.

    Should I also repeat my suggestion about using ^ in plain text?
    Last edited by emakarov; August 20th 2012 at 08:27 AM.
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  4. #19
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    Re: linear and quadratic convergence

    Y, all on the net write so, but I just dont understand how do we GET this! Till now I just have to lern it by memory! I cross the whole net, but cant find the simple explanation that I miss! What would be the definition? Ok, it is area, but I cant move from it!
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  5. #20
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    Re: linear and quadratic convergence

    Quote Originally Posted by marijakopljar View Post
    Y, all on the net write so, but I just dont understand how do we GET this!
    By "this" do you mean the following question:
    Quote Originally Posted by marijakopljar View Post
    How do we get that antiderivative frm x2 = 1/3 x3???
    By definition, an antiderivative of f is a function F such that F' = f. Since \left(\frac{1}{3}x^3\right)'=x^2, the function \frac{1}{3}x^3 is by definition an antiderivative of x^2.

    Quote Originally Posted by marijakopljar View Post
    What would be the definition? Ok, it is area, but I cant move from it!
    Definition of what? The definition of antiderivative is not an area. It is related to area by the Fundamental theorem of calculus.
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  6. #21
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    Re: linear and quadratic convergence

    By definition?
    But, why?
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  7. #22
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    Re: linear and quadratic convergence

    You ignored my two questions in post #20; why should I answer your incomplete questions?
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