Question Number 143268 by Study last updated on 12/Jun/21
$${li}\underset{{x}\rightarrow\infty} {{m}}\left(\frac{{x}+\mathrm{3}}{{x}−\mathrm{4}}\right)^{−\mathrm{2}} =? \\ $$
Answered by SumanKarmakar2007 last updated on 12/Jun/21
$$\mathrm{1} \\ $$$$ \\ $$
Answered by justtry last updated on 12/Jun/21
$$\frac{{lim}}{{x}\rightarrow\infty}\:\left(\frac{\mathrm{1}}{\frac{\left({x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{9}\right)×\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}{\left({x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{16}\right)×\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}}\right) \\ $$$$\frac{\mathrm{1}}{\left(\frac{\mathrm{1}+\mathrm{0}+\mathrm{0}}{\mathrm{1}−\mathrm{0}+\mathrm{0}}\right)}=\mathrm{1} \\ $$