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Use Newton's method to approximate a root of the equation 3sin(x)=x as follows.

Let x1=1 be the initial approximation.
The second approximation x2 is
and the third approximation x3 is

I got x2=-1.454
but can't get x3 :(

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3 answers
  1. You are on the right track!
    x1=1,
    x2=-1.455,
    x3=-3.787,
    x4=-2.140,
    ...
    eventually it will settle on x=-2.28.

    Remember that in the case of multiple roots, the one obtained by Newton's method is very dependent on the initial approximation. I assumed x1=1 is in radians.

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  2. I agree with drwls's setup in
    Newton's method

    starting with x1=1 I also got
    x2= -41.454 but then I got the next values as

    x3 = -3.787
    x4 = -2.1404
    x5 = -2.2878
    x6 = -2.1813
    x7 = -2.283
    etc
    appears to converge to around x = -2.28
    check:
    3sin(-2.28) = -2.2766

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  3. there was supposed to be a reference to
    drwls setup in
    http://www.jiskha.com/display.cgi?id=1283845535

    As you can see in MathMate's reply both of our results coincide.

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