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Math Help - help with limits

  1. #1
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    help with limits

    Hi

    I need help with the following limit:

    \displaystyle\lim_{a\to0} \dfrac{\ln(r/a)}{\ln(b/a)}

    where a < r < b and that a,b are constants.

    thanks in advance
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  2. #2
    Member Mentia's Avatar
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    Apply L'Hopital's rule.

    Note the numerator can be written: ln(r) - ln(a), and similarly the denominator can be written: ln(b) - ln(a).

    The derivative with respect to a of the numerator and the denominator are both: -\frac{1}{a}

    So the limit becomes:

     \lim_{a->0 } \frac{-\frac{1}{a}}{-\frac{1}{a}} = 1
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  3. #3
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    Quote Originally Posted by august View Post
    Hi

    I need help with the following limit:

    \displaystyle\lim_{a\to0} \dfrac{\ln(r/a)}{\ln(b/a)}

    where a < r < b and that a,b are constants.

    thanks in advance
    Can you check what the question should actually say? If a→0 then a is not a constant.
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  4. #4
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    a is a constant but what happens in the limit as it goes to zero?
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  5. #5
    Member Mentia's Avatar
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    Apply L'Hopital's rule. You can check your answer by plugging in random positive numbers for r and b and then putting in a small number for a and checking it in your calculator.
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