Question Number 75795 by ~blr237~ last updated on 17/Dec/19 $$\mathrm{Find}\:\mathrm{out}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{argsh}\left(\mathrm{x}\right)}{\mathrm{x}}\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 18/Dec/19 $${let}\:{A}\:=\int_{\mathrm{0}} ^{\infty}…
Question Number 141328 by mnjuly1970 last updated on 17/May/21 $$……\:{Evaluate}: \\ $$$$\:\:\:\:\:\mathscr{F}\::=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \zeta\left({n}\right)}{{n}+\mathrm{1}}\:=? \\ $$$$……. \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 141320 by mnjuly1970 last updated on 17/May/21 $$\:\:\:\:\:\:\:……{nice}\:……{calculuus}….. \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} \frac{\mathscr{A}\:{rctan}\left({x}^{\mathrm{2}} {y}^{\mathrm{2}} \right)}{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }{dxdy}=\frac{\pi^{\mathrm{2}} \sqrt{\mathrm{2}}}{\mathrm{16}} \\ $$$$…..…
Question Number 75793 by ~blr237~ last updated on 17/Dec/19 $$\mathrm{Prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{arctanx}}{\mathrm{x}\sqrt{\mathrm{log2}}}\right)^{\mathrm{2}} \mathrm{dx}=\:\pi \\ $$ Commented by mathmax by abdo last updated on 18/Dec/19 $${let}\:{I}\:=\int_{\mathrm{0}}…
Question Number 141322 by mnjuly1970 last updated on 17/May/21 $$\:\:\:\:\:……{advanced}……..{calculus}……. \\ $$$$\:{prove}\:{that}:: \\ $$$$\:\:\:\xi:=\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}{e}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)^{{n}^{\mathrm{2}} } =\frac{\pi}{{e}\sqrt{{e}}} \\ $$$$ \\ $$ Terms of…
Question Number 75762 by aliesam last updated on 16/Dec/19 $${if}\:\:{y}\:{cos}\left({x}\right)+{x}\:{cos}\left({y}\right)\:=\:\pi \\ $$$$ \\ $$$${find}\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:\:\:,\:{x}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 141294 by bemath last updated on 17/May/21 $${Find}\:{max}\:\&\:{min}\:{value}\:{of} \\ $$$$\:{f}\left({x}\right)=\frac{{x}}{{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{9}}. \\ $$ Answered by MJS_new last updated on 17/May/21 $$\frac{{df}}{{dx}}=\frac{−{x}^{\mathrm{2}} +\mathrm{9}}{\left({x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{9}\right)^{\mathrm{2}}…
Question Number 141274 by mnjuly1970 last updated on 17/May/21 $$\:\:\:\:\:\:\:\:\:\:\:…….\:{elementary}\:…..{calculus}…….. \\ $$$$\:\:\:\:\:{if}\:\:\:{f}\left({x}\right):=\frac{\sqrt[{\mathrm{3}}]{\left({x}^{\mathrm{3}} +{x}−\mathrm{2}\right)\left(\mathrm{2}{x}^{\mathrm{2}} +{x}−\mathrm{3}\right)\left(\mathrm{1}−{x}^{\mathrm{3}} \right)}}{\left(\mathrm{2}+{cos}\left(\pi{x}\right)\right)^{\mathrm{3}} } \\ $$$$\:\:\:\:\:\:{then}\:\:\:{f}\:'\left(\mathrm{0}\:\right)=?\:\:\&\:{f}\:'\left(\mathrm{1}\right)=? \\ $$$$ \\ $$ Answered by mindispower…
Question Number 141269 by ajfour last updated on 17/May/21 $$\theta+\phi+\psi=\pi\:\:\left({angles}\:{of}\:{a}\:\bigtriangleup\right) \\ $$$${find}\:{maximum}\:{of} \\ $$$$\:\left(\phi−\theta\right)^{\mathrm{2}} +\left(\psi−\phi\right)^{\mathrm{2}} +\left(\psi−\theta\right)^{\mathrm{2}} \:. \\ $$ Commented by MJS_new last updated on…
Question Number 75639 by aliesam last updated on 14/Dec/19 Answered by $@ty@m123 last updated on 14/Dec/19 $${x}={y}\mathrm{cos}\:{y}\:….\left(\mathrm{1}\right) \\ $$$${Differentiating}\:{w}.{r}.{t}.\:{x}, \\ $$$$\mathrm{1}=\left\{{y}\left(−\mathrm{sin}\:{y}\right)+\mathrm{cos}\:{y}\right\}{y}' \\ $$$$\frac{\mathrm{1}}{{y}'}=\mathrm{cos}\:{y}−{y}\mathrm{sin}\:{y}\:….\left(\mathrm{2}\right) \\ $$$${Multiplying}\:\left(\mathrm{2}\right)\:{by}\:{y},…