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Math Help - newton's method

  1. #1
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    Question newton's method

    use newtons method to find the roots of the equation

    sinx=x^(2)+3^(x)-1

    correct to sic decimal places
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by thecount View Post
    use newtons method to find the roots of the equation

    sinx=x^(2)+3^(x)-1

    correct to sic decimal places
    Newton's methof gives us an itterative methof for finding a root of the equation f(x)=0. This is:

    x_{n+1}=x_n-\frac{f(x)}{f'(x)}

    So for this we have:

    f(x)=x^2+3^x-1-\sin(x)

    with:

    f'(x)=2x+\ln(3)3^x-\cos(x)

    Now you need an initial guess, well there is an obvious root at x=0, and a bit of investigation suggests that there is another root to the left of this, so we could take an initial guess x=-1.

    CB
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  3. #3
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    You should understand the theory behind this method, but here is a cool online tool to help check if you're doing it correctly.

    Newton's Method

    Don't cheat though!
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