Math- Calculus

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Use Newton’s Method with initial approximation x1 = 2 to solve the equation x5 +x= 6 . Go to x3,
and tell me how good you think the approximation is. Round all answers to 3 decimal places.

  • Math- Calculus -

    let f(x) = x^5+x-6

    newton's method says
    xn+1 = xn - f(xn)/f'(xn)

    f'(x) = 5x^4 + 1

    so x2 = x1 - f(x1)/f'(x1)
    = 2 - 28/81
    = 1.65432

    then x3 = 1.65432 - .209237
    = 1.44508

    x4 = 1.3685
    x5 = 1.35942
    x6 = 1.359304105
    x7 = 1.359304086
    x8 = 1.359304086 Ok then !!!

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