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Homework Help: Intermediate Value Theorem Excercise

  1. Sep 24, 2009 #1
    If f(x) = x^2 + 10sinx, show that there is a number c such that f(c) = 1000

    Well since I was not given an interval to find a root on, I decided to set the equation equal to 1000 and solve it.

    My work:
    f(x)=x^2 + 10sinx=1000
    x^2 = 1000-10sinx
    x= +/- (1000 - sinx)^1/2
  2. jcsd
  3. Sep 24, 2009 #2


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    Homework Helper

    That is a transcendental equation... you're not going to be able to find an analytic solution. My suggestion: Since 10sin(x) is bounded between -10 and +10, you know that the answer will be in the interval √990 and √1010. Now apply the intermediate value theorem to that interval.
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