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Math Help - Evaluating this limit....

  1. #1
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    Evaluating this limit....

    Question: Evaluate limx->pi/3 sqrt[sin(5x/2)]

    So by using direct substitution that would become sqrt[sin(2.618)].
    sin(2.618) = 0.5
    limit = sqrt(0.5)

    This just feels wrong. Did I do the process incorrectly?
    Any help is appreciated!
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  2. #2
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    I don't see anything wrong with it, other than claiming certain decimals are equal when they're not. Your final answer is correct, and the overall logic is correct, but it's better to use exact numbers along the way when you can.
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  3. #3
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    Also remember that \sqrt{0.5} = \sqrt{\frac{1}{2}}

     = \frac{\sqrt{1}}{\sqrt{2}}

     = \frac{1}{\sqrt{2}}

     = \frac{\sqrt{2}}{2}.
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  4. #4
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    Quote Originally Posted by iluvmathbutitshard View Post
    Question: Evaluate limx->pi/3 sqrt[sin(5x/2)]

    So by using direct substitution that would become sqrt[sin(2.618)].
    sin(2.618) = 0.5
    limit = sqrt(0.5)

    This just feels wrong. Did I do the process incorrectly?
    Any help is appreciated!
    \sqrt{\sin(5\pi/6)}=\sqrt{\sin(\pi-\pi/6)}=\sqrt{\sin(\pi/6)}

    and \pi/6 is 30^{\circ} so \sin(\pi/6)=1/2

    CB
    Last edited by CaptainBlack; September 18th 2010 at 06:47 AM.
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  5. #5
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    \sqrt{\sin(5\pi/6)}=\sqrt{\sin(-\pi/6)}=\sqrt{\sin(\pi/6)}
    Not sure about that equality. I'd agree with this:

    \sqrt{\sin(5\pi/6)}=\sqrt{\sin(\pi/6)}, since the sin function is symmetric about \pi/2.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by Ackbeet View Post
    Not sure about that equality. I'd agree with this:

    \sqrt{\sin(5\pi/6)}=\sqrt{\sin(\pi/6)}, since the sin function is symmetric about \pi/2.
    Fixed now

    CB
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