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Math Help - L'hopital's Rule.

  1. #1
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    L'hopital's Rule.

    I have to use l'hopital's rule to show that for any fixed t, the limit as omega approaches 1, for  \frac{2}{1-\omega^2} (cos(\omega t) - cos(t) ) = tsin(t)

    To do this, I assume I must differentiate with respect to omega, so that means I am allowed to take t as a constant value?

    Even if I am, I can't seem to be able to get there.. Any help would be greatly appreciated, cheers.
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  2. #2
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    Quote Originally Posted by U-God View Post
    I have to use l'hopital's rule to show that for any fixed t, the limit as omega approaches 1, for  \frac{2}{1-\omega^2} (cos(\omega t) - cos(t) ) = tsin(t)

    To do this, I assume I must differentiate with respect to omega, so that means I am allowed to take t as a constant value?

    Even if I am, I can't seem to be able to get there.. Any help would be greatly appreciated, cheers.
    Aha, so you have to do the DE that way.

    Yes, you differentiate wrt \omega, which means you treat t as a constant:


     \lim_{\omega \rightarrow 1} \frac{2(\cos (\omega t) - \cos t}{1 - \omega^2} = \lim_{\omega \rightarrow 1} \frac{2 (- t \sin (\omega t) - 0)}{-2 \omega} = \lim_{\omega \rightarrow 1} \frac{-2 t \sin (\omega t)}{-2 \omega} = \, ....
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  3. #3
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    Thanks again mr fantastic,
    I don't know why I couldn't do that!! I haven't done limits all semester and I was trying to differentiate the function as a whole, not the top and bottom individually.

    Cheers,
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