Math

Find the real root of the equation 3x-cosx-1=0 correct to four decimal places using the Newton Raphson Method.

  1. 👍
  2. 👎
  3. 👁
  1. let y = 3x - cosx - 1
    y' = 3 + sinx

    newx = oldx - (3oldx - cos(oldx) - 1)/(3 + sin(oldx))
    let's take a look
    http://www.wolframalpha.com/input/?i=plot+y+%3D+3x-cosx-1
    it appears x = .5 could be a good start
    x ..... newx
    .5 ---- .6085..
    .6085 .60710
    .60710 .60710 <---- same result correct to 5 decimals

    check in original:
    LS = 3(.60710) - cos(60710) - 1
    = -.0000058... , not bad

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. mathematics

    Find a real root of the equation cos(x) = 3x − 1 correct to four decimal places by using method of successive approximation.

  2. Math

    Use Regula Falsi Method to find a real root of the equation xe^x - 2=0 correct to two decimal places within the interval [0,1].

  3. Calc

    Find the linear approximation of the function g(x) = fifth root(1 + x) at a = 0. g(x)≈ 1+(x/5) Correct: Your answer is correct. Use it to approximate the numbers fifth root (0.95) and fifth root (1.1) (Round your answers to

  4. Pure Mathematics

    Find the modulus and principal argument of the complex numbers giving the argument in radians either as pi or a decimal correct to 2 decimal places c) i square root 3 -2 ALL UPON -2-i square root 3

  1. calculus

    3x4 − 8x3 + 5 = 0, [2, 3] (a) Explain how we know that the given equation must have a root in the given interval. Let f(x) = 3x4 − 8x3 + 5. The polynomial f is continuous on [2, 3], f(2) = < 0, and f(3) = > 0, so by the

  2. Math

    Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 7^4x = 4.9

  3. Algebra 2a

    Help please! 1. What are the real or imaginary solutions of the polynomial equation? x^4-52x^2+576=0 A) 4,-4 B) 4,-6 C) 4,-4,6,-6 D) no solutions 2. What are the real or imaginary solutions of the polynomial equation? x^3=216 A)

  4. Calculus 1

    Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y = (x − 5)^2 that is closest to the origin.

  1. calculus

    Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y = (x − 7)2 that is closest to the origin.

  2. Pre Calc

    Write an equation to a polynomial function that has the following properties: Fourth degree equation Lead coefficient is -2 Two negative real roots and one positive real root The positive real root has multiplicity of 2

  3. Calc 1

    Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y =(x − 5)^2 that is closest to the origin.

  4. Applied Calculus......

    Use the method of bisection to find the root of the equation x^5 + 3x − 7 = 0 accurate to two decimal places.

You can view more similar questions or ask a new question.