Question Number 219440 by Nicholas666 last updated on 25/Apr/25 $$ \\ $$$$\:\:\:{I}=\int\mathrm{tan}\left(\frac{\mathrm{cos}\left({n}\right)}{{n}\left(\mathrm{1}−\mathrm{cos}\left({n}\right)\:+\:\mathrm{cos}^{\mathrm{2}} \left({n}\right)\right)}\right)\:{dn} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 219461 by alcohol last updated on 25/Apr/25 $${I}_{{n}} \:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{x}}{\left({x}\:+\:\mathrm{1}\right)^{{n}} }{dx} \\ $$$${find}\:{I}_{\mathrm{0}} \:{and}\:{I}_{\mathrm{1}} \\ $$$${express}\:{I}_{{n}} \:{interms}\:{of}\:{n}\:{for}\:{all}\:{n}\:\geqslant\:\mathrm{2} \\ $$ Answered by y0o0o…
Question Number 219456 by Nicholas666 last updated on 25/Apr/25 $$ \\ $$$$\:\int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \:\frac{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +{x}_{\mathrm{3}} +{x}_{\mathrm{4}}…
Question Number 219458 by Nicholas666 last updated on 25/Apr/25 $$ \\ $$$$\:\int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \:{x}_{\mathrm{1}} ^{\:\mathrm{2}} {x}_{\mathrm{2}} ^{\:\mathrm{3}} {x}_{\mathrm{3}} ^{\:\mathrm{4}}…
Question Number 219459 by Tawa11 last updated on 25/Apr/25 Two cups m and n contains the same mass of water, m is at 25°c while…
Question Number 219423 by SdC355 last updated on 24/Apr/25 Answered by SdC355 last updated on 24/Apr/25 $$\overset{\rightarrow} {\boldsymbol{\mathcal{S}}}\left({u},{v}\right)=\begin{cases}{\frac{\mathrm{5}}{\mathrm{4}}\left(\mathrm{1}−\frac{{v}}{\mathrm{2}\pi}\right)\mathrm{cos}\left(\mathrm{2}{v}\right)\left(\mathrm{1}+\mathrm{cos}\left({u}\right)\right)+\mathrm{cos}\left(\mathrm{2}{v}\right)}\\{\frac{\mathrm{5}}{\mathrm{4}}\left(\mathrm{1}−\frac{{v}}{\mathrm{2}\pi}\right)\mathrm{sin}\left(\mathrm{2}{v}\right)\left(\mathrm{1}+\mathrm{cos}\left({u}\right)\right)+\mathrm{sin}\left(\mathrm{2}{v}\right)}\\{\frac{\mathrm{10}{v}}{\mathrm{2}\pi}+\frac{\mathrm{5}}{\mathrm{4}}\left(\mathrm{1}−\frac{{v}}{\mathrm{2}\pi}\right)\mathrm{sin}\left({u}\right)}\end{cases} \\ $$$$\mathrm{0}\leq{u}\leq\mathrm{2}\pi\:,\:−\pi\leq{v}\leq\mathrm{2}\pi \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)=−{x}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −{y}\overset{\rightarrow}…
Question Number 219414 by universe last updated on 24/Apr/25 $$\:\:\:\mathrm{given}\:\mathrm{the}\:\mathrm{recursive}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{define}\:\mathrm{by}\:\mathrm{setting} \\ $$$$\:\:\mathrm{a}_{\mathrm{1}\:} \:\in\:\left(\mathrm{0},\mathrm{1}\right)\:\:\:,\:\:\:\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\mathrm{a}_{\mathrm{n}} \left(\mathrm{1}−\mathrm{a}_{\mathrm{n}} \right)\:\:\:,\:\mathrm{n}\geqslant\mathrm{1} \\ $$$$\:\:\mathrm{prove}\:\mathrm{that}\:\:\left(\mathrm{1}\right)\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{na}_{\mathrm{n}} =\:\mathrm{1} \\ $$$$\:\:\left(\mathrm{2}\right)\:\:\mathrm{b}_{\mathrm{n}} \:=\:\mathrm{n}\left(\mathrm{1}−\mathrm{na}_{\mathrm{n}} \right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{incresing}\:\mathrm{sequence}…
Question Number 219408 by CrispyXYZ last updated on 24/Apr/25 $${a}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}.\:{a}_{{n}} =\frac{\mathrm{2}}{{n}+\mathrm{3}}+\left(\mathrm{1}−\frac{\mathrm{1}}{{n}+\mathrm{3}}\right)^{\mathrm{2}} {a}_{{n}−\mathrm{1}} . \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{of}\:{a}_{{n}} . \\ $$ Answered by SdC355 last updated on…
Question Number 219404 by golsendro last updated on 24/Apr/25 $$\:\:\mathrm{given}\:\mathrm{g}\left(\mathrm{x}\right)=\:\frac{\mathrm{x}−\mathrm{2023}}{\mathrm{x}−\mathrm{1}} \\ $$$$\:\:\mathrm{find}\:\left(\mathrm{gogogogogog}\right)\left(\mathrm{2024}\right) \\ $$ Commented by kapoorshah last updated on 25/Apr/25 $${g}^{−\mathrm{1}} \left({x}\right)=\frac{{x}−\mathrm{2023}}{{x}−\mathrm{1}} \\ $$$$\:\:\:\:\:\left({g}\:{o}\:{g}\:{o}\:{g}\:{o}\:{g}\:{o}\:{g}\:{o}\:{g}\right)\left(\mathrm{2024}\right)…