Question Number 209434 by justenspi last updated on 10/Jul/24
$${Help} \\ $$
Commented by justenspi last updated on 10/Jul/24
Commented by Berbere last updated on 10/Jul/24
$$=\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{e}^{{g}\left({x}\right)} \left({e}^{{f}\left({x}\right)−{g}\left({x}\right)} −\mathrm{1}\right)}{{f}\left({x}\right)−{g}\left({x}\right)} \\ $$$$={e}^{{g}\left({a}\right)} \ast\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{e}^{{h}\left({x}\right)} −\mathrm{1}}{{h}\left({x}\right)} \\ $$$${x}\rightarrow{a}\:{h}\left({x}\right)\rightarrow\mathrm{0} \\ $$$$\Rightarrow{e}^{{g}\left({a}\right)} .\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{{x}} −\mathrm{1}}{{x}}={e}^{{a}} \\ $$$$ \\ $$$$ \\ $$
Commented by justenspi last updated on 10/Jul/24
$${Thank}\:{you}\:{Sir}\:{Witcher}\:{you}\:{are}\:{the}\:{best} \\ $$
Commented by justenspi last updated on 10/Jul/24
Commented by justenspi last updated on 10/Jul/24
$${Also}\:{sir}\:{in}\:{this}\:{problem}\:{shouldnot}\:{the}\:{final} \\ $$$${answer}\:{be}\:{a}\:{function}\:{in}\:{n} \\ $$$${why}\:{did}\:{he}\:{assume}\:{that}\:{n}=\mathrm{1010} \\ $$