Category: Limits

Question Number 29689 by mrW2 last updated on 11/Feb/18 $$find\underset{x\to 0}{\lim }{\left(\frac{2}{1+a^x}\right)}^{\frac{1}{x}}=?$$ Commented by abdo imad last updated on 13/Feb/18 $${let}\:{put}\:{A}\left({x}\right)=\left(\frac{\mathrm{2}}{\mathrm{1}+{a}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}}}…

Question Number 95133 by john santu last updated on 23/May/20 $$\underset{x\to \mathrm{\infty }}{\lim }({\mathrm{x}}^2.{\mathrm{e}}^{-2\mathrm{x}})=?$$ Answered by bobhans last updated on 23/May/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{2}}…

Question Number 160604 by cortano last updated on 03/Dec/21 $$\:\:\mathrm{S}_{\mathrm{n}} =\:\frac{\mathrm{12}}{\left(\mathrm{4}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)\left(\mathrm{4}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)}+\frac{\mathrm{12}^{\mathrm{2}} }{\left(\mathrm{4}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)\left(\mathrm{4}^{\mathrm{3}} −\mathrm{3}^{\mathrm{3}} \right)}+\frac{\mathrm{12}^{\mathrm{3}} }{\left(\mathrm{4}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)\left(\mathrm{4}^{\mathrm{4}} −\mathrm{3}^{\mathrm{4}} \right)}+…+\frac{\mathrm{12}^{\mathrm{n}}…

Question Number 29511 by abdo imad last updated on 09/Feb/18 $$find{lim}_{n\to +\mathrm{\infty }}\frac{{(n!)}^2}{\left(2n\right)!}.$$ Commented by prof Abdo imad last updated on 12/Feb/18 $${let}\:{use}\:{stirling}\:{formula}\:{we}\:{have}…

Question Number 29509 by abdo imad last updated on 09/Feb/18 $$find{lim}_{n\to +\mathrm{\infty }}\frac{n!}{2^{n-1}}.$$ Commented by abdo imad last updated on 11/Feb/18 $${let}\:{use}\:{stirling}\:{formula}\:\:{n}!\:\sim\:{n}^{{n}} \:{e}^{−{n}}…