Question Number 167295 by mnjuly1970 last updated on 12/Mar/22 Answered by qaz last updated on 12/Mar/22 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\left(\mathrm{2n}\right)!}{\mathrm{n}^{\mathrm{n}} \mathrm{n}!}\right)^{\mathrm{1}/\mathrm{n}} \\ $$$$=\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\mathrm{2n}\right)!}{\mathrm{n}^{\mathrm{n}} \mathrm{n}!}\centerdot\frac{\left(\mathrm{n}−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} \left(\mathrm{n}−\mathrm{1}\right)!}{\left(\mathrm{2n}−\mathrm{2}\right)!} \\…
Question Number 167289 by qaz last updated on 12/Mar/22 $$\mathrm{calculate}\:::\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{n}^{\frac{\mathrm{1}}{\mathrm{k}}} =\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 167280 by puissant last updated on 11/Mar/22 Commented by puissant last updated on 11/Mar/22 $${Area}=\:??? \\ $$ Answered by som(math1967) last updated on…
Question Number 167277 by cortano1 last updated on 11/Mar/22 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{3}} −\mathrm{3x}+\mathrm{3arctan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{5}} }\:=? \\ $$ Answered by qaz last updated on 11/Mar/22 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}^{\mathrm{3}} −\mathrm{3x}+\mathrm{3arctan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{5}}…
Question Number 167160 by qaz last updated on 08/Mar/22 $$\mathrm{calculate}\:::\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}ncos}\left(\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{sin}\:\left(\mathrm{2}\pi\mathrm{nx}\right)}{\mathrm{x}}\mathrm{dx}\right)=\frac{\mathrm{1}}{\mathrm{2}\pi} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 101615 by john santu last updated on 03/Jul/20 Commented by bramlex last updated on 03/Jul/20 $$\mathrm{i}\:\mathrm{got}\:−\infty\:\mathrm{sir}\: \\ $$ Commented by john santu last…
Question Number 101610 by bramlex last updated on 03/Jul/20 Answered by john santu last updated on 04/Jul/20 $$\mathrm{L}'\mathrm{Hopital} \\ $$$$\Leftrightarrow\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} +\mathrm{5}}}{\mathrm{sin}\:\mathrm{2}{x}}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}}{\mathrm{sin}\:\mathrm{2}{x}}\:×\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}\sqrt{{x}^{\mathrm{3}}…
Question Number 167105 by mnjuly1970 last updated on 06/Mar/22 $$ \\ $$$$\:\:\:\:\mathrm{I}{f}\:\:\:\:{g}\left({x}\right)=\:\begin{cases}{\:{x}^{\:\mathrm{2}} \:\:\:\:\:{x}\geqslant\mathrm{1}}\\{\:{x}^{\:\mathrm{3}} \:\:\:\:\:\:\:{x}<\:\mathrm{1}}\end{cases}\: \\ $$$$\:\:\:\:\:\:{then}\:\:\:\:\:{lim}_{\:{h}\rightarrow\:\mathrm{0}^{\:+} } \frac{\:{g}\:\left(\mathrm{1}+\mathrm{3}{h}\:\right)\:−\:{g}\:\left(\mathrm{1}−\mathrm{5}{h}\:\right)}{{h}}\:=? \\ $$ Answered by greogoury55 last updated…
Question Number 167100 by qaz last updated on 06/Mar/22 $$\mathrm{calculate}\:\:\:::\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{\int_{\mathrm{0}} ^{\mathrm{x}} \mathrm{cos}\:^{\mathrm{n}} \left(\frac{\mathrm{1}}{\mathrm{t}}\right)\mathrm{dt}}{\mathrm{x}}=? \\ $$ Commented by mindispower last updated on 09/Mar/22 $${i}\:{deleat}\:{my}\:{solution}\:{i}\:{see}\:{my}\:{error}…
Question Number 36018 by math1967 last updated on 27/May/18 $${Find}\:{the}\:{value}\:{of} \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {{lim}}\:\frac{{sinx}−\left({sinx}\right)^{{sinx}} }{\mathrm{1}−{sinx}+{lnsinx}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 27/May/18 $${t}=\frac{\Pi}{\mathrm{2}}−{x}\: \\…