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Thread: Newton's method to approximate the intersection...

  1. #1
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    Newton's method to approximate the intersection...

    Find the third approximation of x3 of Newton's method to approximate the intersection of $\displaystyle y=[\sqrt(x)]+1$ and $\displaystyle y=x^2$.

    What do I do? Set them equal to each other?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by hazecraze View Post
    Find the third approximation of x3 of Newton's method to approximate the intersection of $\displaystyle y=[\sqrt(x)]+1$ and $\displaystyle y=x^2$.

    What do I do? Set them equal to each other?
    Yes, and then get everything on one side of the equation. That will be the $\displaystyle f(x)$ you need to apply Newton's Method.

    Can you take it from here?
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  3. #3
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    So I did $\displaystyle f(x)=x^2-\sqrt(x)-1$
    $\displaystyle f'(x)= 2x-\frac{1}{2\sqrt(x)}$

    I used $\displaystyle x1=1$

    $\displaystyle x2= 1 + \frac{1-1-1}{2-.5}$

    = .333

    $\displaystyle x3=.333 + \frac{-1.466}{-.8660}$

    =$\displaystyle 2.0227$
    Answer is supposed to be: $\displaystyle 1.50143$
    Last edited by hazecraze; Dec 5th 2009 at 09:25 AM.
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  4. #4
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    I tried it again and now I'm getting 7.68, which is even further from the right answer. What am I doing wrong?
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  5. #5
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    optimization problem

    edit
    Last edited by hazecraze; Dec 5th 2009 at 10:39 AM. Reason: wrong thread
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  6. #6
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    Looks like you made a mistake with a sign
    $\displaystyle
    x2= 1 - \frac{1-1-1}{2-.5}
    $
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