Question Number 86328 by M±th+et£s last updated on 28/Mar/20 $$\int\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }}\:{dx} \\ $$ Answered by TANMAY PANACEA. last updated on 28/Mar/20 $$\int\frac{\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}{\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 86326 by ~blr237~ last updated on 28/Mar/20 $${Let}\:{f}\:{a}\:{continue}\:{function}\:{acknowleding} \\ $$$$\alpha\:{as}\:{a}\:{fix}\:{point}\:{on}\:\left[\mathrm{0},\mathrm{1}\right].{F}\:\:{a}\:{function}\:{such}\:{as}\:\frac{{dF}}{{dx}}={f}\left({x}\right) \\ $$$$\forall\:{n}\:,\:\:{u}_{{n}+\mathrm{1}} =\frac{{F}\left({u}_{{n}} \right)−{F}\left(\alpha\right)}{{u}_{{n}} −\alpha}\: \\ $$$${Prove}\:{that}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{u}_{{n}} \:=\alpha \\ $$ Terms of…
Question Number 151860 by maged last updated on 23/Aug/21 $$\underset{\mathrm{1}} {\overset{\mathrm{5}} {\int}}\mid\mathrm{2}−\mid\mathrm{3}−\boldsymbol{\mathrm{x}}\mid\mid\mathrm{dx} \\ $$ Commented by lyubita last updated on 23/Aug/21 $${It}\:{means}\:{area}\:{bounded}\:{by}\:{the}\:{graph} \\ $$$${and}\:{x}\:{axis}\:{between}\:{x}\:=\:\mathrm{1}\:{and}\:{x}\:=\:\mathrm{5} \\…
Question Number 151863 by pticantor last updated on 23/Aug/21 $$\: \\ $$$$\boldsymbol{{li}}\underset{\boldsymbol{{x}}−\mathrm{0}} {\boldsymbol{{m}}}\frac{\mathrm{1}−\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\prod}}\boldsymbol{{cos}}\left(\boldsymbol{{kx}}\right)}{\boldsymbol{{x}}^{\mathrm{2}} }=???? \\ $$$$ \\ $$ Answered by ArielVyny last updated…
Question Number 86324 by TawaTawa1 last updated on 28/Mar/20 $$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\frac{\mathrm{1}\:}{\:\sqrt{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}}\:\:\:+\:\:\sqrt{\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}}}\:\boldsymbol{\mathrm{dx}} \\ $$ Commented by MJS last updated on 28/Mar/20 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{exactly}\:\mathrm{solve}\:\mathrm{this}… \\ $$ Commented…
Question Number 20786 by Tinkutara last updated on 02/Sep/17 $$\mathrm{Two}\:\mathrm{particles}\:{A}\:\mathrm{and}\:{B}\:\mathrm{start}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{position}\:\mathrm{along}\:\mathrm{the}\:\mathrm{circular}\:\mathrm{path}\:\mathrm{of} \\ $$$$\mathrm{radius}\:\mathrm{0}.\mathrm{5}\:\mathrm{m}\:\mathrm{with}\:\mathrm{a}\:\mathrm{speed}\:{v}_{{A}} \:=\:\mathrm{1}\:\mathrm{ms}^{−\mathrm{1}} \\ $$$$\mathrm{and}\:{v}_{{B}} \:=\:\mathrm{1}.\mathrm{2}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{in}\:\mathrm{opposite}\:\mathrm{direction}. \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{time}\:\mathrm{before}\:\mathrm{they}\:\mathrm{collide}. \\ $$ Answered by…
Question Number 151859 by puissant last updated on 23/Aug/21 Commented by OlafThorendsen last updated on 23/Aug/21 $$\left.\mathrm{1}\right) \\ $$$${U}_{{n}} \:=\:\int_{\mathrm{0}} ^{\pi} \mathrm{sin}^{\mathrm{2}{n}} {t}\:{dt} \\ $$$${U}_{\mathrm{0}}…
Question Number 20785 by Tinkutara last updated on 02/Sep/17 $$\mathrm{If}\:\mathrm{in}\:\mathrm{a}\:\Delta{ABC},\:\mathrm{tan}\frac{{A}}{\mathrm{2}},\:\mathrm{tan}\frac{{B}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{tan}\frac{{C}}{\mathrm{2}} \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{HP},\:\mathrm{then}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{cot}\frac{{B}}{\mathrm{2}}\:\mathrm{is}\:\mathrm{greater}\:\mathrm{than} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{2}\sqrt{\mathrm{3}} \\ $$$$\left(\mathrm{2}\right)\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$$\left(\mathrm{3}\right)\:\sqrt{\mathrm{3}} \\ $$$$\left(\mathrm{4}\right)\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$ Answered…
Question Number 151858 by mathdanisur last updated on 23/Aug/21 Answered by Olaf_Thorendsen last updated on 23/Aug/21 $${f}\left({x}\right)\:=\:\mathrm{sin}{x}+\frac{\mathrm{sin3}{x}}{\mathrm{3}}+\frac{\mathrm{sin5}{x}}{\mathrm{5}}+\mathrm{sin}\frac{\mathrm{7}{x}}{\mathrm{7}} \\ $$$${f}'\left({x}\right)\:=\:\mathrm{cos}{x}+\mathrm{cos3}{x}+\mathrm{cos5}{x}+\mathrm{cos7}{x} \\ $$$${f}'\left({x}\right)\:=\:\mathrm{Re}\left({e}^{{ix}} +{e}^{\mathrm{3}{ix}} +{e}^{\mathrm{5}{ix}} +{e}^{\mathrm{7}{ix}} \right)…
Question Number 151849 by mathdanisur last updated on 23/Aug/21 Commented by Rasheed.Sindhi last updated on 23/Aug/21 $${Special}\:{general}\:{case} \\ $$$${x}={y}={z}\left({prime}\:{of}\:\mathrm{4}{m}+\mathrm{3}\:{type}\right) \\ $$$$\frac{{z}^{\mathrm{2}{k}} +{z}^{\mathrm{2}{k}} }{{z}^{{k}} +{z}^{{k}} }=\frac{\mathrm{2}{z}^{\mathrm{2}{k}}…