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Math Help - 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 y=[\sqrt(x)]+1 and 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 y=[\sqrt(x)]+1 and 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 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 f(x)=x^2-\sqrt(x)-1
    f'(x)= 2x-\frac{1}{2\sqrt(x)}

    I used x1=1

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

    = .333

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

    = 2.0227
    Answer is supposed to be: 1.50143
    Last edited by hazecraze; December 5th 2009 at 10:25 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; December 5th 2009 at 11:39 AM. Reason: wrong thread
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  6. #6
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    Looks like you made a mistake with a sign
    <br />
x2= 1 - \frac{1-1-1}{2-.5}<br />
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