Question Number 184341 by Davidtim last updated on 05/Jan/23
$${li}\underset{{x}\rightarrow\infty} {{m}}\frac{{x}^{\mathrm{2}} }{\mathrm{3}^{{x}} }=? \\ $$
Commented by JDamian last updated on 05/Jan/23
zero, as the denominator tends to infinity faster than the numerator does.
Answered by SEKRET last updated on 05/Jan/23
$$\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\boldsymbol{\mathrm{lim}}}\:\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\mathrm{3}^{\boldsymbol{\mathrm{x}}} }=\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\boldsymbol{\mathrm{lim}}}\:\frac{\mathrm{2}\boldsymbol{\mathrm{x}}}{\mathrm{3}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{ln}}\left(\mathrm{3}\right)}=\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\boldsymbol{\mathrm{lim}}}\frac{\mathrm{2}}{\mathrm{3}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{ln}}^{\mathrm{2}} \left(\mathrm{3}\right)}=\mathrm{0} \\ $$