Question Number 27327 by Giannibo last updated on 05/Jan/18
$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{x}^{\mathrm{2n}} }{\mathrm{1}+\mid\mathrm{x}\mid+\mathrm{x}^{\mathrm{4n}} } \\ $$
Commented by abdo imad last updated on 05/Jan/18
$$=\:{lim}_{{n}−>\propto} \:\:\:\:\frac{/{x}/^{\mathrm{2}{n}} }{/{x}/^{\mathrm{4}{n}} \left(\:\:\:/{x}/^{−\mathrm{4}{n}} \:+\:/{x}/^{−\mathrm{3}{n}} +\mathrm{1}\right)} \\ $$$$={lim}_{{n}−>\propto\:\:} \:\:\frac{\mathrm{1}}{/{x}/^{\mathrm{2}{n}} }.\:\:\:\frac{\mathrm{1}}{/{x}/^{−\mathrm{4}{n}} +/{x}/^{−\mathrm{3}{n}} \:+\mathrm{1}} \\ $$
Commented by abdo imad last updated on 05/Jan/18
$${lim}\:\left(….\right)=\mathrm{0} \\ $$
Commented by prakash jain last updated on 05/Jan/18
$$\mathrm{Does}\:\mathrm{it}\:\mathrm{matter}\:\mathrm{if}\:\mid{x}\mid<\mathrm{1}\:\mathrm{or}\:\mid{x}\mid>\mathrm{1} \\ $$$$\mathrm{or}\:\mid{x}\mid=\mathrm{1}? \\ $$
Commented by abdo imad last updated on 05/Jan/18
$${yes}\:{yesif}\:/{x}/<\mathrm{1}\:\:\:{lim}\left(…\right)=\mathrm{0} \\ $$$${if}\:/{x}/=\mathrm{1}\:\:\:{lim}\left(…\right)=\frac{\mathrm{1}}{\mathrm{3}}\:\:{i}\:{don}\:{t}\:{give}\:{attention}\:{to}\:{this}\:{case}. \\ $$