Question Number 120301 by TITA last updated on 30/Oct/20
$${is}\:{it}\:{possible}\:{to}\:{have}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{4}} }\right)\:{please}\:{help} \\ $$
Commented by Dwaipayan Shikari last updated on 30/Oct/20
$${When} \\ $$$${x}\rightarrow\infty \\ $$
Commented by bemath last updated on 30/Oct/20
$${in}\:{limit}\:{it}\:{is}\:{possible}. \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{1}\pm\:{f}\left({x}\right)\right)^{{n}} \:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}\pm{n}\:{f}\left({x}\right)\right) \\ $$
Commented by Bird last updated on 30/Oct/20
$${if}\:\:{f}\left({x}\right)\rightarrow\mathrm{0}\:{when}\:{x}\rightarrow\mathrm{0}\:{we}\:{get} \\ $$$$\left(\mathrm{1}+{f}\left({x}\right)\right)^{{n}} \sim\mathrm{1}+{nf}\left({x}\right) \\ $$
Answered by Bird last updated on 30/Oct/20
$${for}\:{x}\rightarrow\infty\:\:\left({very}\:{big}\:{value}\right) \\ $$