Results 1 to 2 of 2

Math Help - Newtons method

  1. #1
    Newbie
    Joined
    Dec 2008
    From
    Pennington gap
    Posts
    16

    Unhappy Newtons method

    WORK OUT!

    Use Newton's method to solve cos(3x)-2x+1=0. Show the values of each iteration until you have reached the " best" solution your calculator can display
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    Let f(x) = cos(3x)-2x+1 with a representative curve Cf

    Start from say x_0 = 0
    Then x_1 is the abscissa of the intersection point between the x axis and the tangent to the curve Cf at the point whose abscissa is x_0

    f'(x) = -3 sin(3x)-2
    The equation of the tangent to Cf at the point of abscissa x_n is
    y = (-3 sin(3 x_n) - 2) (x - x_n) + cos(3 x_n) - 2 x_n + 1

    x_{n+1} is given by
    0 = (-3 sin(3 x_n) - 2) (x_{n+1} - x_n) + cos(3 x_n) - 2 x_n + 1

    x_{n+1} = x_n + \frac{cos(3 x_n) - 2 x_n + 1}{3 sin(3 x_n) + 2}

    Start for example from x_0 = 0 and then use a calculator to iterate and find the best estimation of the solution
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Newtons method help?
    Posted in the Differential Geometry Forum
    Replies: 15
    Last Post: December 13th 2010, 10:33 PM
  2. Newtons Method
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 15th 2010, 11:57 AM
  3. Newtons Method Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 4th 2008, 06:03 AM
  4. Newtons Method
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 12th 2008, 05:21 AM
  5. Newtons Method
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 28th 2007, 12:17 AM

Search Tags


/mathhelpforum @mathhelpforum