Question Number 96319 by M±th+et+s last updated on 31/May/20 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\left(\frac{\left(\mathrm{1}+{x}\right)^{\frac{\mathrm{1}}{{x}}} }{{e}}\right)^{\frac{\mathrm{1}}{{x}}} \\ $$ Answered by abdomathmax last updated on 31/May/20 $$\mathrm{f}\left(\mathrm{x}\right)=\left(\frac{\left(\mathrm{1}+\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} }{\mathrm{e}}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \:\Rightarrow\mathrm{ln}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\frac{\mathrm{1}}{\mathrm{x}}\mathrm{ln}\left(\frac{\left(\mathrm{1}+\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} }{\mathrm{e}}\right)…
Question Number 30758 by abdo imad last updated on 25/Feb/18 $${find}\:{lim}_{{n}\rightarrow\infty} \left(\frac{\mathrm{1}}{{n}+\mathrm{1}}\:+\frac{\mathrm{1}}{{n}+\mathrm{2}}\:+….+\frac{\mathrm{1}}{{n}+{p}}\right)\:{pfixed}\:{fromN}^{\bigstar} \\ $$$$ \\ $$ Commented by abdo imad last updated on 28/Feb/18 $${let}\:{put}\:{u}_{{n}}…
Question Number 30759 by abdo imad last updated on 25/Feb/18 $${find}\:{lim}_{{n}\rightarrow\infty} \:\:\:\:\left(\frac{{n}!}{{n}^{{n}} }\right)^{\frac{\mathrm{1}}{{n}}} \:. \\ $$ Commented by abdo imad last updated on 27/Feb/18 $${let}\:{use}\:{the}\:{stirling}\:{formula}\:{we}\:{have}…
Question Number 30757 by abdo imad last updated on 25/Feb/18 $${find}\:{lim}_{{n}\rightarrow\infty} \:\:\left(\frac{\mathrm{1}}{{n}}\:+\frac{\mathrm{1}}{\:\sqrt{{n}^{\mathrm{2}} \:−\mathrm{1}}}\:+….\:+\frac{\mathrm{1}}{\:\sqrt{{n}^{\mathrm{2}} \:−\left({n}−\mathrm{1}\right)^{\mathrm{2}} }}\:\right) \\ $$ Commented by abdo imad last updated on 28/Feb/18…
Question Number 30755 by abdo imad last updated on 25/Feb/18 $${find}\:\:\:{lim}_{{n}\rightarrow\infty} \:\:^{{n}} \sqrt{\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\left(\mathrm{1}+\frac{\mathrm{2}}{{n}}\right)…\left(\mathrm{1}+\frac{{n}}{{n}}\right)\:} \\ $$ Commented by abdo imad last updated on 28/Feb/18 $${let}\:{put}\:{A}_{{n}} =^{{n}}…
Question Number 161801 by qaz last updated on 22/Dec/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{n}} ^{\mathrm{n}\left(\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{n}}\right)^{\mathrm{n}} } \left(\mathrm{1}−\frac{\mathrm{4}}{\mathrm{x}}\right)^{\mathrm{x}} \mathrm{dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 96232 by joki last updated on 30/May/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{cos}\:\sqrt{{x}}−\mathrm{cos}\:{x}}{\mathrm{1}−\mathrm{cos}\:\sqrt{{x}}}= \\ $$ Commented by bobhans last updated on 31/May/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\sqrt{\mathrm{x}}−\mathrm{cos}\:\mathrm{x}}{\mathrm{1}−\mathrm{cos}\:\sqrt{\mathrm{x}}\:}\:=\:\mathrm{does}\:\mathrm{not}\:\mathrm{exist}\:! \\ $$ Answered…
Question Number 161770 by cortano last updated on 22/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }+\mathrm{2}{x}\right)^{\mathrm{2021}} −\left(\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }−\mathrm{2}{x}\right)^{\mathrm{2021}} }{{x}} \\ $$ Answered by Ar Brandon last updated on 22/Dec/21…
Question Number 96222 by bobhans last updated on 30/May/20 $$\mathrm{If}\:\mathrm{for}\:\mathrm{nonzero}\:{x}\:;\:\mathrm{2}{f}\:\left({x}^{\mathrm{2}} \right)+\mathrm{3}{f}\:\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)\:=\:{x}^{\mathrm{2}} −\mathrm{1} \\ $$$${then}\:{f}\:\left({x}^{\mathrm{2}} \right)\:=\:? \\ $$ Commented by bobhans last updated on 31/May/20…
Question Number 161760 by cortano last updated on 22/Dec/21 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:{x}}{\:\sqrt[{\mathrm{3}}]{\left(\mathrm{1}−\mathrm{cos}\:{x}\right)^{\mathrm{2}} }}\:=? \\ $$ Answered by Ar Brandon last updated on 22/Dec/21 $$\mathscr{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{tan}{x}}{\:\sqrt[{\mathrm{3}}]{\left(\mathrm{1}−\mathrm{cos}{x}\right)^{\mathrm{2}} }}=\underset{{x}\rightarrow\mathrm{0}}…