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Math Help - limit/l'hopital

  1. #1
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    limit/l'hopital



    lim
    x->1 \frac{3ax-3a}{2(x-1)}

    ^I think the error is here, because if I simplify it, there is no where to do l'hopital.
    x->1 \frac{3a(x-1)}{2(x-1)}

    x->1 \frac{3a}{2}
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  2. #2
    Super Member Deadstar's Avatar
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    The derivative of the top line should be...
    3ax^{3a-1} - 3a
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  3. #3
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    so f' of numerator and denominator = \frac{(3a)(3a -1)[(3ax)^(3a-2)]}{2} ?
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  4. #4
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    I simplified it to this,:
    but no luck.
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  5. #5
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    Quote Originally Posted by hazecraze View Post


    lim
    x->1 \frac{3ax-3a}{2(x-1)}

    ^I think the error is here, because if I simplify it, there is no where to do l'hopital.
    x->1 \frac{3a(x-1)}{2(x-1)}

    x->1 \frac{3a}{2}
    \lim_{x \to 1}\frac{x^{3a} - 3ax + 3a - 1}{(x - 1)^2} = \lim_{x \to 1}\frac{3ax^{3a - 1} - 3a}{2(x - 1)}.

    This is still indeterminate, so use L'Hospital again...

     = \lim_{x \to 1}\frac{3a(3a - 1)x^{3a - 2}}{2}

     = \frac{3a(3a - 1)}{2}

     = \frac{9a^2 - 3a}{2}.
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