Question Number 10830 by Saham last updated on 26/Feb/17
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3}^{\mathrm{x}} \:−\:\mathrm{3}^{−\mathrm{x}} }{\mathrm{3}^{\mathrm{x}} \:+\:\mathrm{3}^{−\mathrm{x}} } \\ $$
Answered by bahmanfeshki last updated on 26/Feb/17
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{3}^{{x}} \left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}{x}} }\right)}{\mathrm{3}^{{x}} \left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}{x}} }\right)}=\mathrm{1} \\ $$
Answered by FilupS last updated on 27/Feb/17
$${L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{3}^{{x}} −\mathrm{3}^{−{x}} }{\mathrm{3}^{{x}} +\mathrm{3}^{−{x}} } \\ $$$${L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{3}^{−\mathrm{2}{x}} }{\mathrm{1}+\mathrm{3}^{−\mathrm{2}{x}} }=\frac{\mathrm{1}−\mathrm{0}}{\mathrm{1}+\mathrm{0}} \\ $$$${L}=\mathrm{1} \\ $$
Commented by Saham last updated on 27/Feb/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$