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March 25, 2017

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use a graphing utility to solve each equation, rounded to 2 decimal places

1. x^2 - 2sin2x = 3x

2. x^2 = x + 3cos2x

  • Trig - ,

    I don't have a graphing utility. If you don't either, use a hand calculator and iterate until you get x close enough to satsfying the equation. x=0 is one solution of the first equation. There is anotherin the vicinity of x=3.
    If x = 3, x^2 - 2 sin 2x - 3x = 0.558
    If x = 2.9, x^2 - 2 sin 2x - 3x = 0.174
    If x = 2.8, x^2 - 2 sin 2x - 3x = 0.071
    If x = 2.7, x^2 - 2 sin 2x - 3x = -0.037
    If x = 2.74 x^2 - 2 sin 2x - 3x = 0.007
    Try x = 2.73. You can get closer by further iteration and interpolating

    Use a similar method to solve the other equation

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