Question Number 74600 by rajesh4661kumar@gmail.com last updated on 27/Nov/19
Answered by ajfour last updated on 27/Nov/19
![L=lim_(x→0) [{(((a^(mx) −1)/(mx)))/(((b^(nx) −1)/(nx)))}(((mx)/(nx)))] L = ((mln a)/(nln b)) .](https://www.tinkutara.com/question/Q74603.png)
$${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[\left\{\left(\frac{{a}^{{mx}} −\mathrm{1}}{{mx}}\right)/\left(\frac{{b}^{{nx}} −\mathrm{1}}{{nx}}\right)\right\}\left(\frac{{mx}}{{nx}}\right)\right] \\ $$$$\:{L}\:=\:\frac{{m}\mathrm{ln}\:{a}}{{n}\mathrm{ln}\:{b}}\:. \\ $$