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Find the three zeros for the following function on the interval -5 </= x </= 5
(1 + 50sin(x)) / (x^2 + 3)

  • Calculus -

    For the expression to be zero,
    1 + 50sinx = 0
    sinx = -1/50

    x = π +.02 or 2π - .02
    x = 3.1616 or 6.263
    the period of 50sinx is 2π, so adding or subtracting 2π to the above answers will produce more answers

    3.1616+2π ---> beyond domain
    3.1616-2π = -3.1216
    6.263-2π = -.02
    so for -5 ≤ x ≤ 5
    x = -3.1216 , -.02, 3.1216

  • Calculus -

    Thank you, this helps tremendously!

  • Calculus -

    How did you come up with 3.1216 positive. I've tried to come up with this number but I can't figure it out. Also, it doesn't make 1 + 50 sin(x) = 0.

  • Calculus -

    It was a copy error.
    As you can see from the 5th line, I had x = 3.1616

    so the final answers are
    x = -3.1216 , -.02, and 3.1616

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