lim-x-ln-ax-b-ln-bx-a-

Question Number 1368 by prakash jain last updated on 25/Jul/15

\lim_{x \to \infty} \frac{\ln (a x + b)}{\ln (b x + a)} = ?

Commented by 123456 last updated on 25/Jul/15

f (x) = \frac{\ln (a x + b)}{\ln (b x + a)}

\frac{\frac{d}{d x} [\ln (a x + b)]}{\frac{d}{d x} [\ln (b x + a)]} = \frac{\frac{a}{a x + b}}{\frac{b}{b x + a}} = \frac{a (b x + a)}{b (a x + b)} \to \frac{a b}{b a} = 1

Answered by 112358 last updated on 25/Jul/15

L = \lim_{x \to \infty} \frac{l n (a x + b)}{l n (b x + a)} = \frac{\infty}{\infty} w h i c h i s i n d e t e r m i n a t e .

P e r h a p s L^{'} H {\hat{o p t i a l}}^{'} s r u l e c a n b e u s e d .

Commented by 123456 last updated on 26/Jul/15

a > 0, b > 0

Facebook Tweet Pin