1. ## 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.

2. 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:

$\lim_{a->0 } \frac{-\frac{1}{a}}{-\frac{1}{a}} = 1$

3. Originally Posted by august
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.

Can you check what the question should actually say? If a→0 then a is not a constant.

4. a is a constant but what happens in the limit as it goes to zero?

5. 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.