Hi
I need help with the following limit:
$\displaystyle \displaystyle\lim_{a\to0} \dfrac{\ln(r/a)}{\ln(b/a)}$
where a < r < b and that a,b are constants.
thanks in advance
Apply L'Hopital's rule.
Note the numerator can be written: $\displaystyle ln(r) - ln(a)$, and similarly the denominator can be written: $\displaystyle ln(b) - ln(a)$.
The derivative with respect to a of the numerator and the denominator are both: $\displaystyle -\frac{1}{a}$
So the limit becomes:
$\displaystyle \lim_{a->0 } \frac{-\frac{1}{a}}{-\frac{1}{a}} = 1$