Menu Close

lim-x-x-x-2-1-x-3-1-1-3-2x-1-3-




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

Leave a Reply

Your email address will not be published. Required fields are marked *