Question Number 164702 by mathls last updated on 20/Jan/22 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\left(\frac{\mathrm{1}^{{x}} +\mathrm{2}^{{x}} +\centerdot\centerdot\centerdot+{n}^{{x}} }{{n}}\right)^{\frac{\mathrm{1}}{{x}}} =? \\ $$ Answered by mahdipoor last updated on 21/Jan/22 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 33595 by abdo imad last updated on 19/Apr/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{ln}\left(\mathrm{1}+{sinx}\right)\:−{x}\sqrt{\mathrm{1}−{x}}}{{sinx}\:−{shx}}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33593 by abdo imad last updated on 19/Apr/18 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{\mathrm{2}\left(\mathrm{1}−{cosx}\right){sinx}\:−{x}^{\mathrm{3}} \:\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{4}}} }{{sin}^{\mathrm{5}} {x}\:−{x}^{\mathrm{5}} } \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 33594 by abdo imad last updated on 19/Apr/18 $${calculate}\:\:{lim}_{{x}\rightarrow\mathrm{1}^{−} } \:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{\alpha} }\left({arcsinx}\:−\frac{\pi}{\mathrm{2}}\right)\:. \\ $$ Commented by abdo imad last updated on 24/Apr/18 $${let}\:{use}\:{the}\:{ch}.\:\mathrm{1}−{x}\:={t}\:\Rightarrow{lim}_{{x}\rightarrow\mathrm{1}^{−}…
Question Number 164585 by mnjuly1970 last updated on 19/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathcal{I}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\mathrm{Li}_{\:\mathrm{2}} \:\left(\:{x}\:\right)}{\mathrm{1}\:+\:{x}}\:{dx}\:=\:? \\ $$$$\:\:\:\:−−−−−−\: \\ $$ Answered by mindispower last updated on…
Question Number 164530 by hoochhoch last updated on 18/Jan/22 Commented by Rasheed.Sindhi last updated on 18/Jan/22 $$\mathrm{sin}\alpha=−\frac{\mathrm{12}}{\mathrm{3}}=−\mathrm{4}\Rightarrow\alpha\notin\mathbb{R}\:{in}\:{Q}#\mathrm{1} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 98986 by Ar Brandon last updated on 17/Jun/20 $$\mathrm{Is}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{u}_{\mathrm{n}} =\mathrm{cos}\left(\frac{\mathrm{n}\pi}{\mathrm{20}}\right)\:\mathrm{divergent}? \\ $$ Answered by maths mind last updated on 17/Jun/20 $${u}_{\mathrm{40}{n}+\mathrm{10}} =\mathrm{0} \\…
Question Number 98952 by Ar Brandon last updated on 17/Jun/20 $$\mathrm{Without}\:\mathrm{using}\:\mathrm{L}'\mathrm{H}\hat {\mathrm{o}pital}'\mathrm{s}\:\mathrm{rule}\:\mathrm{or}\:\mathrm{Maclaurin}'\mathrm{s}\:\mathrm{expansion} \\ $$$$\mathrm{series},\:\mathrm{find}\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\frac{\mathrm{xe}^{\mathrm{x}} }{\mathrm{e}^{\mathrm{x}} −\mathrm{1}}−\mathrm{1}}{\mathrm{x}} \\ $$ Commented by 675480065 last updated on…
Question Number 98955 by Ar Brandon last updated on 17/Jun/20 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\centerdot\centerdot\centerdot}}}} \\ $$ Commented by mr W last updated on 17/Jun/20 $$=\:{Q}\mathrm{98858} \\ $$…
Question Number 98938 by john santu last updated on 17/Jun/20 Answered by mathmax by abdo last updated on 17/Jun/20 $$=\mathrm{lim}_{\mathrm{n}\rightarrow\infty} \frac{\mathrm{n}^{\mathrm{2}} \left(\mathrm{3}+\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}}\right)\left(\mathrm{2}+\frac{\mathrm{5}}{\mathrm{n}}\right)}{\mathrm{n}^{\mathrm{2}} \left(\mathrm{7}+\frac{\mathrm{2}}{\mathrm{n}}\right)\left(\mathrm{5}−\frac{\mathrm{cosn}}{\mathrm{n}}\right)}\:=\frac{\mathrm{3}×\mathrm{2}}{\mathrm{7}×\mathrm{5}}\:=\frac{\mathrm{6}}{\mathrm{35}} \\…