Question Number 106240 by pticantor last updated on 03/Aug/20 $$ \\ $$$$ \\ $$$$ \\ $$$$\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow+\infty} {\boldsymbol{{m}}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{{k}}+\mathrm{1}} }{\boldsymbol{{k}}}=???? \\ $$ Answered by Dwaipayan…
Question Number 106237 by Study last updated on 03/Aug/20 Answered by Dwaipayan Shikari last updated on 03/Aug/20 $$\frac{\mathrm{1}}{{n}}\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left({e}^{\frac{\mathrm{1}}{{n}}} +{e}^{\frac{\mathrm{2}}{{n}}} +….+{e}^{\frac{{n}}{{n}}} \right) \\ $$$$\frac{\mathrm{1}}{{n}}\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{r}=\mathrm{1}}…
Question Number 106217 by bobhans last updated on 03/Aug/20 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{and}\:\mathrm{f}\left(\mathrm{0}\right)=\mathrm{0}\:\mathrm{when}\:\mathrm{x} \\ $$$$=\:\mathrm{0}\:,\mathrm{what}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\underset{\mathrm{0}} {\overset{\mathrm{t}} {\int}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}}{\mathrm{t}^{\mathrm{2}} } \\ $$$$ \\ $$ Answered by john santu…
Question Number 40667 by Tawa1 last updated on 25/Jul/18 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{g}\left(\mathrm{x}\right)\:\:\mathrm{must}\:\mathrm{have},\:\mathrm{if}\:\mathrm{g}\:\mathrm{complies}\:\mathrm{the}\:\mathrm{statement}\: \\ $$$$\mathrm{about}\:\mathrm{limit}.\:\mathrm{Suppose}\:\:\:\underset{{x}\rightarrow\:−\mathrm{4}} {\mathrm{lim}}\:\:\left[\mathrm{x}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\mathrm{g}\left(\mathrm{x}\right)\right]\:\:=\:\:\mathrm{2} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 26/Jul/18 $${mobile}\:{handset}\:{does}\:{not}\:{show}\:{a}\:{few}\:…
Question Number 106173 by john santu last updated on 03/Aug/20 $$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\left(\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} \mathrm{cot}\:^{\mathrm{2}} \mathrm{x}}\right)\:? \\ $$ Answered by bemath last updated on 03/Aug/20 $$\mathrm{set}\:\mathrm{x}\:=\:\frac{\pi}{\mathrm{2}}+\flat\:\rightarrow\frac{\mathrm{4}}{\pi^{\mathrm{2}} }×\underset{\flat\rightarrow\mathrm{0}}…
Question Number 106175 by john santu last updated on 03/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{x}}−\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}}}\:=\:? \\ $$ Answered by bemath last updated on 03/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{x}}−\sqrt{\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{6}}}}{\mathrm{x}^{\mathrm{2}}…
Question Number 171706 by Haisokheng last updated on 20/Jun/22 Answered by cortano1 last updated on 20/Jun/22 Answered by thfchristopher last updated on 20/Jun/22 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{1}−{x}^{\mathrm{3}}…
Question Number 171705 by Haisokheng last updated on 20/Jun/22 Answered by puissant last updated on 20/Jun/22 $$=\:\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}} ^{\pi} {cos}^{\mathrm{2}} \left(\mathrm{2}{x}\right){dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}\pi}\int_{\mathrm{0}} ^{\pi} \mathrm{1}+{cos}\left(\mathrm{4}{x}\right){dx} \\…
Question Number 106152 by bemath last updated on 03/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{xcos}\:\mathrm{2xcos}\:\mathrm{3x}…\mathrm{cos}\:\mathrm{nx}}{\mathrm{x}^{\mathrm{n}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 106101 by O Predador last updated on 02/Aug/20 Answered by Dwaipayan Shikari last updated on 02/Aug/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt{\mathrm{2}+\frac{\mathrm{1}}{{x}}}−\frac{\mathrm{3}}{\:\sqrt{{x}}}}{\:\sqrt{\mathrm{1}−\frac{\mathrm{2}}{{x}}}−\frac{\sqrt{\mathrm{2}}}{\:\sqrt{{x}}}}=\frac{\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{1}}}=\sqrt{\mathrm{2}} \\ $$ Commented by O…