Question Number 25221 by chernoaguero@gmail.com last updated on 06/Dec/17
$$\mathrm{Find}\:\mathrm{the}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\:\frac{\mathrm{e}^{\mathrm{x}} }{\sqrt{\mathrm{e}^{\mathrm{2x}} +\mathrm{1}}} \\ $$
Answered by jota+ last updated on 06/Dec/17
$$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{1}/{e}^{{x}} \right){e}^{{x}} }{\left(\mathrm{1}/\sqrt{{e}^{\mathrm{2}{x}} }\right)\sqrt{{e}^{\mathrm{2}{x}} +\mathrm{1}}}\:\:= \\ $$$$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}\:}{\sqrt{\mathrm{1}+\mathrm{1}/{e}^{\mathrm{2}{x}} }}\:\:\:=\:\mathrm{1}\: \\ $$$$ \\ $$
Commented by chernoaguero@gmail.com last updated on 06/Dec/17
$$\mathrm{plzz}\:\mathrm{show}\:\mathrm{working} \\ $$
Commented by prakash jain last updated on 06/Dec/17
$$\mathrm{Divide}\:\mathrm{numerator}\:\mathrm{and}\:\mathrm{denominator} \\ $$$$\mathrm{by}\:{e}^{{x}} \\ $$
Commented by chernoaguero@gmail.com last updated on 07/Dec/17
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{i}\:\mathrm{have}\:\mathrm{seen}\:\mathrm{it}\:\mathrm{now} \\ $$