Question Number 209434 by justenspi last updated on 10/Jul/24
![Help](https://www.tinkutara.com/question/Q209434.png)
$${Help} \\ $$
Commented by justenspi last updated on 10/Jul/24
![](https://www.tinkutara.com/question/34399.png)
Commented by Berbere last updated on 10/Jul/24
![=lim_(x→a) ((e^(g(x)) (e^(f(x)−g(x)) −1))/(f(x)−g(x))) =e^(g(a)) ∗lim_(x→a) ((e^(h(x)) −1)/(h(x))) x→a h(x)→0 ⇒e^(g(a)) .lim_(x→0) ((e^x −1)/x)=e^a](https://www.tinkutara.com/question/Q209440.png)
$$=\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{e}^{{g}\left({x}\right)} \left({e}^{{f}\left({x}\right)−{g}\left({x}\right)} −\mathrm{1}\right)}{{f}\left({x}\right)−{g}\left({x}\right)} \\ $$$$={e}^{{g}\left({a}\right)} \ast\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{e}^{{h}\left({x}\right)} −\mathrm{1}}{{h}\left({x}\right)} \\ $$$${x}\rightarrow{a}\:{h}\left({x}\right)\rightarrow\mathrm{0} \\ $$$$\Rightarrow{e}^{{g}\left({a}\right)} .\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{{x}} −\mathrm{1}}{{x}}={e}^{{a}} \\ $$$$ \\ $$$$ \\ $$
Commented by justenspi last updated on 10/Jul/24
![Thank you Sir Witcher you are the best](https://www.tinkutara.com/question/Q209466.png)
$${Thank}\:{you}\:{Sir}\:{Witcher}\:{you}\:{are}\:{the}\:{best} \\ $$
Commented by justenspi last updated on 10/Jul/24
![](https://www.tinkutara.com/question/34408.png)
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=1010](https://www.tinkutara.com/question/Q209468.png)
$${Also}\:{sir}\:{in}\:{this}\:{problem}\:{shouldnot}\:{the}\:{final} \\ $$$${answer}\:{be}\:{a}\:{function}\:{in}\:{n} \\ $$$${why}\:{did}\:{he}\:{assume}\:{that}\:{n}=\mathrm{1010} \\ $$