Question Number 118088 by bobhans last updated on 15/Oct/20
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}.\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:.\sqrt[{\mathrm{3}\:}]{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{3}} }\:=? \\ $$
Answered by bemath last updated on 15/Oct/20
$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}.\sqrt{\mathrm{x}^{\mathrm{2}} }.\sqrt[{\mathrm{3}\:}]{\mathrm{x}^{\mathrm{3}} }}{\mathrm{8x}^{\mathrm{3}} }\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{8x}^{\mathrm{3}} }\:=\:\frac{\mathrm{1}}{\mathrm{8}} \\ $$