Question Number 130423 by john_santu last updated on 25/Jan/21 $$\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}\sqrt{{x}}}{\mathrm{3}{x}}\right)−\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{\mathrm{1}−{x}}\:\right)=\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}}\right) \\ $$ Answered by liberty last updated on 25/Jan/21 $$\:{let}\:{p}\:=\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{3}\sqrt{{x}}}\right)\:;\:{q}=\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{\mathrm{1}−{x}}\:\right)…
Question Number 64886 by mathmax by abdo last updated on 22/Jul/19 $${let}\:{f}\left({x}\right)\:={cos}\left(\frac{\mathrm{1}}{{x}}\right)\:\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:{at}\:{x}_{\mathrm{0}} =\frac{\mathrm{3}}{\pi} \\ $$ Terms of Service Privacy Policy…
Question Number 130416 by mohammad17 last updated on 25/Jan/21 $${find}\:{singular}\:{point}\:{for}\:{each}\: \\ $$$$ \\ $$$$\left(\mathrm{1}\right){f}\left({z}\right)=\frac{{e}^{{z}} }{{z}^{\mathrm{2}} }\:\:\:\:\:\:\:,\:\:\:\:\left(\mathrm{2}\right){f}\left({z}\right)=\frac{{sinz}}{{z}}\:\:\:, \\ $$$$ \\ $$$$\left(\mathrm{3}\right){f}\left({z}\right)=\frac{\mathrm{1}−{cosz}}{{sinz}^{\mathrm{2}} }\:\:\:\:\:,\:\:\:\left(\mathrm{4}\right){f}\left({z}\right)={ln}\mid{z}\mid \\ $$$$ \\ $$$${how}\:{can}\:{solve}\:{this}\:{help}\:{me}\:{sir}…
Question Number 130417 by Lordose last updated on 25/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sin}\left(\alpha\mathrm{x}\right)\mathrm{sin}\left(\beta\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on 25/Jan/21 $$\mathrm{I}\:=\int_{\mathrm{0}}…
Question Number 130415 by Dwaipayan Shikari last updated on 25/Jan/21 $$\frac{\pi}{{e}}{sin}\left(\mathrm{1}\right)−\frac{\pi^{\mathrm{2}} }{\mathrm{2}{e}^{\mathrm{2}} }{sin}\left(\mathrm{2}\right)+\frac{\pi^{\mathrm{3}} }{\mathrm{3}{e}^{\mathrm{3}} }{sin}\left(\mathrm{3}\right)−\frac{\pi^{\mathrm{4}} }{\mathrm{4}{e}^{\mathrm{4}} }{sin}\left(\mathrm{4}\right)+… \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 64873 by mathmax by abdo last updated on 22/Jul/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{{x}+{sint}}\:\:\:{with}\:{xreal} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{\left({x}+{sint}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral} \\…
Question Number 64872 by Rio Michael last updated on 22/Jul/19 $${Given}\:{that}\: \\ $$$$\:{y}\:=\:\left({cosx}^{} \right)^{{sinx}} \:\:{find}\:\frac{{dy}}{{dx}} \\ $$$${and}\: \\ $$$$\:\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:{y} \\ $$ Commented by kaivan.ahmadi…
Question Number 130406 by john_santu last updated on 25/Jan/21 $$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\mathrm{cos}\:\left(\mathrm{2}{x}+\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{2}}+{x}\right)=?\right. \\ $$ Commented by Dwaipayan Shikari last updated on 25/Jan/21 $$−\mathrm{1} \\ $$ Answered…
Question Number 64871 by Rio Michael last updated on 22/Jul/19 $${any}\:{hint}\:{about}\:{how}\:{to}\:{prove}\:{by}\:{induction}\:{in}\:{the}\:{Sigma}\:{notion}\:{topic}? \\ $$$${like}\:{in}\:\Sigma \\ $$ Commented by mathmax by abdo last updated on 22/Jul/19 $${you}\:{question}\:{is}\:{not}\:{clear}….…
Question Number 130402 by pipin last updated on 25/Jan/21 $$\: \\ $$$$\:\int\:\left(\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \right).\left(\frac{\boldsymbol{\mathrm{x}}^{\mathrm{6}} +\boldsymbol{\mathrm{x}}^{\mathrm{5}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{4}} }{\left(\mathrm{1}+\boldsymbol{\mathrm{x}}\right)^{\mathrm{6}} }\right)\boldsymbol{\mathrm{dx}}\:=\:… \\ $$ Terms of Service Privacy Policy Contact:…