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Math Help - Trig Limit #2

  1. #1
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    Trig Limit #2

    Another one that I can 't get:

    \displaystyle \lim_{t\to 0 } \frac {sin^2 3t}{t^2}

    Can I convert this to:

    9 * \displaystyle \lim_{t\to 0 } \frac {sin^2 t}{t^2}

    If so, then the solution seems easy ( 9 * 1 = 9)

    But I suspect that my algebra is faulty.

    Thanks.
    Last edited by mr fantastic; January 23rd 2011 at 01:31 AM. Reason: Title.
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  2. #2
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    Quote Originally Posted by reastland View Post
    Another one that I can 't get:

    \displaystyle \lim_{t\to 0 } \frac {sin^2 3t}{t^2}

    Can I convert this to:

    9 * \displaystyle \lim_{t\to 0 } \frac {sin^2 t}{t^2}

    If so, then the solution seems easy ( 9 * 1 = 9)

    But I suspect that my algebra is faulty.

    Thanks.
    What? How did you get that 9?
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  3. #3
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    (3t)^2 = 9t^2

    I knew that it was wrong. The answer to the question is 9, so I backed into the idea that you could extract the 3^2, but I didn't like it. I think that I'll try \sin{(2t + t)} unless you think that is the wrong direction.
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  4. #4
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    \displaystyle \frac{\sin^2{3t}}{t^2} = \frac{9\sin^2{3t}}{9t^2}

    \displaystyle = 9\left(\frac{\sin{3t}}{3t}\right)^2.


    This should now be easy to evalute.
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  5. #5
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    Quote Originally Posted by reastland View Post
    (3t)^2 = 9t^2

    I knew that it was wrong. The answer to the question is 9, so I backed into the idea that you could extract the 3^2, but I didn't like it. I think that I'll try \sin{(2t + t)} unless you think that is the wrong direction.
    You can't just pull it out like that.
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  6. #6
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    That looks more like the format I was aiming for. Thanks!
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