Question Number 140513 by mathocean1 last updated on 08/May/21 $$\mathrm{n}\:\in\:\mathbb{N}^{\ast} \:\mathrm{and}\:\mathrm{k}\:\in\:\mathbb{N}^{\ast} . \\ $$$$\mathrm{Given}\:\mathrm{0}\leqslant\mathrm{k}\leqslant\mathrm{n}−\mathrm{1}. \\ $$$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{n}}\mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{k}}{\mathrm{n}}\right)\leqslant\underset{\mathrm{1}+\frac{\mathrm{k}}{\mathrm{n}}} {\overset{\mathrm{1}+\frac{\mathrm{k}+\mathrm{1}}{\mathrm{n}}} {\int}}\mathrm{lnx}\:\mathrm{dn}\leqslant\frac{\mathrm{1}}{\mathrm{n}}\mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{k}+\mathrm{1}}{\mathrm{n}}\right) \\ $$ Terms of Service…
Question Number 140503 by ERA last updated on 08/May/21 $$\boldsymbol{\mathrm{P}}\mathrm{rove}\:\mathrm{it} \\ $$$$\sqrt{\boldsymbol{{a}}+\sqrt{\boldsymbol{{b}}}}=\sqrt{\frac{\boldsymbol{{a}}+\sqrt{\boldsymbol{{a}}^{\mathrm{2}} +\boldsymbol{{b}}}}{\mathrm{2}}+}\sqrt{\frac{\boldsymbol{{a}}−\sqrt{\boldsymbol{{a}}^{\mathrm{2}} −\boldsymbol{{b}}}}{\mathrm{2}}} \\ $$ Commented by MJS_new last updated on 08/May/21 $$\mathrm{it}'\mathrm{s}\:\mathrm{wrong} \\…
Question Number 74957 by vishalbhardwaj last updated on 04/Dec/19 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{difference}\:\mathrm{between} \\ $$$$\mathrm{relation}\:\mathrm{and}\:\mathrm{function}\:?? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 9404 by alfat123 last updated on 05/Dec/16 Answered by geovane10math last updated on 06/Dec/16 $$\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{read}… \\ $$$${f}'\left({x}\right)\:=\:\mathrm{2}{x}\:+\:\mathrm{2} \\ $$$$\int{f}'\left({x}\right)\:{dx}\:=\:\int\:\mathrm{2}{x}\:+\:\mathrm{2}\:{dx}\:=\:\int\mathrm{2}{x}\:{dx}\:+\:\int\mathrm{2}\:{dx} \\ $$$$=\:{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\:{C} \\…
Question Number 9407 by geovane10math last updated on 06/Dec/16 $$\pi\:=\:\mathrm{180}°\:=\:\Pi \\ $$$$\pi\:=\:\mathrm{3},\mathrm{141}…\:=\:\pi \\ $$$$\mathrm{Solve}\:\left(\mathrm{find}\:{n}\:\in\:\mathbb{N}\right): \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{k}\centerdot\mathrm{10}^{{n}} \pi\right)}{{k}}\:+\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{k}\centerdot\mathrm{10}^{{n}} {e}\right)}{{k}}\:=\:\mathrm{0} \\ $$$$ \\…
Question Number 140475 by mohammad17 last updated on 08/May/21 $$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{{tan}^{−\mathrm{1}} \left(\sqrt{{tanx}}\right)}{{tanx}}{dx} \\ $$$${how}\:{can}\:{solve}\:{this} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 9403 by alfat123 last updated on 05/Dec/16 Answered by ridwan balatif last updated on 05/Dec/16 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{5x}\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{6}} \mathrm{dx}=\mathrm{u}.\mathrm{v}−\int\mathrm{vdu} \\ $$$$\mathrm{misal}:\:\mathrm{u}=\mathrm{5x}\rightarrow\mathrm{du}=\mathrm{5dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{dv}=\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{6}}…
Question Number 140474 by mathdave last updated on 08/May/21 Answered by MJS_new last updated on 08/May/21 $$\mathrm{obviously}\:{x}=\mathrm{0}\vee{x}=\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 9396 by Shiva last updated on 04/Dec/16 $$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }+\mathrm{4y}=\mathrm{tan}\:\mathrm{2x} \\ $$ Commented by 123456 last updated on 04/Dec/16 $${y}={y}_{{n}} +{y}_{{f}} \\ $$$${y}_{{n}}…
Question Number 140467 by dayladau1234 last updated on 08/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com