Question Number 199393 by Calculusboy last updated on 02/Nov/23 Answered by cortano12 last updated on 03/Nov/23 $$\:\mathrm{A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\frac{\mathrm{x}}{\mathrm{2011}}\right)\left(\mathrm{1}+\frac{\mathrm{2x}}{\mathrm{2012}}\right)\left(\mathrm{1}+\frac{\mathrm{3x}}{\mathrm{2013}}\right)−\mathrm{1}}{\mathrm{x}} \\ $$$$\:\:\mathrm{A}=\:\frac{\mathrm{1}}{\mathrm{2011}}\:+\frac{\mathrm{2}}{\mathrm{2012}}\:+\:\frac{\mathrm{3}}{\mathrm{2013}}\: \\ $$ Commented by essaad…
Question Number 199084 by universe last updated on 27/Oct/23 $$\:\:\:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\sqrt{\mathrm{n}}} \:\left(\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{n}}\right)^{\mathrm{n}} \mathrm{dx}\:\:\:=\:\:\:\:??? \\ $$ Answered by witcher3 last updated on 27/Oct/23 $$\mathrm{x}=\sqrt{\mathrm{n}}.\mathrm{y}…
Question Number 198952 by ArifinTanjung last updated on 26/Oct/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{3x}}{\mathrm{tan}\:\mathrm{6x}}\:=\:….? \\ $$ Answered by Mathspace last updated on 26/Oct/23 $${lim}=\frac{\mathrm{3}}{\mathrm{6}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left({sin}\left(\mathrm{3}{x}\right)\sim\mathrm{3}{x}\:{and}\:{tan}\left(\mathrm{6}{x}\right)\sim\mathrm{6}{x}\right) \\ $$…
Question Number 199012 by universe last updated on 26/Oct/23 $$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{log}\:{n}}{{n}}\:^{\:\:{n}} \sqrt{\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{k}^{{n}} }{{k}!}}\:\:\:=\:\:\:???? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198839 by Guillaume last updated on 24/Oct/23 $${lim}\:{sin}\left({x}\right)\:=\:? \\ $$$${x}\rightarrow+\infty \\ $$ Commented by Frix last updated on 25/Oct/23 $$\mathrm{Does}\:\mathrm{not}\:\mathrm{exist}. \\ $$ Terms…
Question Number 198572 by cortano12 last updated on 22/Oct/23 $$\:\:\:\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2n}}} {\mathrm{lim}}\:\frac{\sqrt{\frac{\mathrm{sin}\:\mathrm{2nx}}{\mathrm{1}+\mathrm{cos}\:\mathrm{nx}}}}{\mathrm{4n}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} −\pi^{\mathrm{2}} }\:=? \\ $$ Answered by MM42 last updated on 22/Oct/23 $$\frac{\pi}{\mathrm{2}{n}}−{x}={u} \\…
Question Number 198254 by mathocean1 last updated on 15/Oct/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198152 by universe last updated on 11/Oct/23 $$\:\:\:\:{a}_{{n}+\mathrm{2}} \:=\:\:\:\sqrt{{a}_{{n}} ×{a}_{{n}+\mathrm{1}} }\:\:\:\forall\:{n}\geqslant\mathrm{1}\:,\:{n}\:\in\:\mathrm{N} \\ $$$$\:\mathrm{and}\:\mathrm{here}\:\:\mathrm{a}_{\mathrm{1}\:} =\:\alpha\:\:{and}\:{a}_{\mathrm{2}} =\:\beta\:\:\mathrm{then} \\ $$$$\:\:\:\mathrm{prove}\:\mathrm{that}\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}+\mathrm{2}} \:\:\:=\:\:\left(\alpha×\beta^{\mathrm{2}} \right)^{\mathrm{1}/\mathrm{3}} \\ $$ Answered…
Question Number 198032 by cortano12 last updated on 08/Oct/23 $$\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{4025x}}}\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}}}\:+\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}+\mathrm{1}}}\:+\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}+\mathrm{2}}\:}\:+…\:+\frac{\mathrm{1}}{\:\sqrt{\mathrm{4025x}}}\:\right)=? \\ $$ Commented by universe last updated on 08/Oct/23 $$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{4025}}}×\frac{\mathrm{1}}{{x}}\underset{{r}=\mathrm{0}} {\overset{\mathrm{4024}{x}} {\sum}}\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{r}/{x}}} \\…
Question Number 197998 by mathlove last updated on 07/Oct/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}−{ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}{{x}^{\mathrm{3}} }=? \\ $$$${with}\:{out}\:{L}'{Hospital}\:{rul} \\ $$ Answered by witcher3 last updated on 07/Oct/23 $$\mathrm{x}=\mathrm{sh}\left(\mathrm{t}\right),\mathrm{t}\rightarrow\mathrm{0}…