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Find the number of solution

  1. Jan 5, 2013 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    The number of solutions of the equation sin x = |x|/10

    2. Relevant equations

    3. The attempt at a solution
    When x>0
    10sinx-x=0
    When x<0
    10sinx+x=0

    But how do I solve the above equations?
     
  2. jcsd
  3. Jan 5, 2013 #2

    Ray Vickson

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    Draw a graph of sin(x) and |x|/10; this will tell you the number of solutions, and will also give you a very rough idea of where the solutions lie.
     
  4. Jan 5, 2013 #3
    IF you only need the number of solutions, and not the solutions themselves, a graph should almost be enough. If you need a little more reasoning, consider:
    a) the maximum value of sine
    b) the sign of |x|/10
    b) the number of possible crossings per sine period.
     
  5. Jan 5, 2013 #4

    haruspex

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    As a useful check, you should be able to see quickly whether the number of solutions with x > 0 is even or odd.
     
  6. Jan 6, 2013 #5

    utkarshakash

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    Thanks
     
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