Question Number 80416 by jagoll last updated on 03/Feb/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{x}\mathrm{cos}\:{x}}{\left(\mathrm{1}+\mathrm{sin}\:{x}\right)^{\mathrm{2}} }\:{dx}\:? \\ $$ Answered by MJS last updated on 03/Feb/20 $$\int\frac{{x}\mathrm{cos}\:{x}}{\left(\mathrm{1}+\mathrm{sin}\:{x}\right)^{\mathrm{2}} }{dx}= \\…
Question Number 80397 by M±th+et£s last updated on 02/Feb/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\:\sqrt[{{y}}]{{x}^{\pi} }\:+\mathrm{1}}\:{dx}\:{dy}\:=\mathrm{2}{c}\: \\ $$$${whrre}\:{c}\:{denote}\:{tha}\:{catalan}^{,} {s}\:{constant} \\ $$ Commented by mathmax…
Question Number 80369 by M±th+et£s last updated on 02/Feb/20 Commented by mathmax by abdo last updated on 03/Feb/20 $${let}\:{A}\:=\int\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} } \:\:\:\left(\mathrm{1}+{u}^{\mathrm{2}} \:+{v}^{\mathrm{2}} \:+{w}^{\mathrm{2}} \right)^{−\mathrm{2}} {dudvdw}…
Question Number 145888 by bramlexs22 last updated on 09/Jul/21 Answered by liberty last updated on 09/Jul/21 $${f}\left({x}\right)={x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c}\:;\:{a},{b},{c}\:\in{R} \\ $$$${f}\:'\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{ax}+{b} \\ $$$${f}\:''\left({x}\right)=\mathrm{6}{x}+\mathrm{2}{a}\: \\…
Question Number 80332 by ~blr237~ last updated on 02/Feb/20 $$\:\:{let}\:\alpha\:\in\mathbb{R}\:\:{and}\:\:\:\:{a}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{sin}\left({k}\alpha\right)}{{n}+{k}} \\ $$$${Find}\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:{a}_{{n}} \: \\ $$ Commented by Rio Michael last updated…
Question Number 80334 by ~blr237~ last updated on 02/Feb/20 $$\:{let}\:\:\:{f}\in{L}^{\mathrm{1}} \left(\mathbb{R}\right)\:\:\: \\ $$$${let}\:\:{u}_{{n}} =\:\int_{{a}} ^{{b}} {f}\left({t}\right){sin}\left({nt}\right){dt}\:,\:{v}_{{n}} =\int_{{a}} ^{{b}} \frac{{f}\left({t}\right)}{{t}}{sin}\left({nt}\right)\: \\ $$$$\left.\mathrm{1}\right){Prove}\:{that}\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{u}_{{n}} =\mathrm{0} \\ $$$$\left.\mathrm{2}\right){Deduce}\:\:{in}\:{term}\:{of}\:{a},{b},{f}\left(\mathrm{0}\right)\:{the}\:{value}\:{of}\:\:\underset{{n}\rightarrow\infty}…
Question Number 80312 by TawaTawa last updated on 02/Feb/20 Commented by mr W last updated on 02/Feb/20 $${what}\:{is}\:\left\{…\right\}\:{here}\:? \\ $$ Commented by TawaTawa last updated…
Question Number 80300 by john santu last updated on 02/Feb/20 Commented by ~blr237~ last updated on 02/Feb/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\:\frac{\mathrm{1}}{{x}}=\mathrm{0}^{−\:\:} \:\:{and}\:\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\:\frac{\mathrm{1}}{{x}}=−\infty\:\: \\ $$$$\left.\underset{{x}\rightarrow\mathrm{0}^{−} }…
Question Number 145828 by ArielVyny last updated on 08/Jul/21 $$\int\frac{\mathrm{1}}{{x}^{\alpha} +{a}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 145827 by qaz last updated on 08/Jul/21 $$\mathrm{Use}\:\mathrm{Abel}\:\mathrm{summation}\:\mathrm{to}\:\mathrm{evaluate}\::: \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2n}−\mathrm{1}\right)\centerdot\mathrm{2}^{\mathrm{n}} }=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{ln}\left(\sqrt{\mathrm{2}}+\mathrm{1}\right) \\ $$ Answered by Ar Brandon last updated on 08/Jul/21…