Question Number 214326 by mathlove last updated on 05/Dec/24
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{4}}]{{x}}−\sqrt[{\mathrm{6}}]{{x}}}{\:\sqrt[{\mathrm{4}}]{{x}}+\sqrt[{\mathrm{6}}]{{x}}}=? \\ $$
Answered by malwan last updated on 05/Dec/24
$${put}\:{y}={x}^{\mathrm{12}} \\ $$$$\underset{{y}\rightarrow\infty} {{lim}}\:\frac{{y}^{\mathrm{3}} −{y}^{\mathrm{2}} }{{y}^{\mathrm{3}} +{y}^{\mathrm{2}} }\:=\:\mathrm{1} \\ $$