Question Number 142898 by islamo last updated on 06/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 142893 by mnjuly1970 last updated on 06/Jun/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…..{mathematical}\:…..{analysis}…… \\ $$$$\:\:\:\:\:\:\:{f}\:\in\:{C}\:\left[\mathrm{0},\mathrm{1}\right]\:{and}\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{{n}} {f}\left({x}\right){dx}=\frac{\mathrm{1}}{{n}+\mathrm{2}}\:,\:{n}\in\mathbb{N} \\ $$$$\:\:\:\:\:\:\:\:{prove}\:\:{f}\left({x}\right):={x}\:….. \\ $$ Answered by mindispower last…
Question Number 11823 by Joel576 last updated on 01/Apr/17 $$\mathrm{3}\:+\:\mathrm{2}\left(\mathrm{3}^{\mathrm{2}} \right)\:+\:\mathrm{3}\left(\mathrm{3}^{\mathrm{3}} \right)\:+\:…\:+\:\mathrm{10}\left(\mathrm{3}^{\mathrm{10}} \right)\:=\:? \\ $$ Answered by ajfour last updated on 02/Apr/17 $${S}=\:\mathrm{3}+\mathrm{2}\left(\mathrm{3}\right)^{\mathrm{2}} +\mathrm{3}\left(\mathrm{3}\right)^{\mathrm{3}} +…+\mathrm{10}\left(\mathrm{3}\right)^{\mathrm{10}}…
Question Number 11822 by Joel576 last updated on 01/Apr/17 $$\int\:\frac{\mathrm{tan}\:{x}}{\mathrm{1}\:+\:\mathrm{sin}\:{x}}\:{dx} \\ $$ Answered by ajfour last updated on 01/Apr/17 $${let}\:{x}=\frac{\pi}{\mathrm{2}}−\theta \\ $$$${I}=\int\frac{\mathrm{tan}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}}{dx}\:=\int\frac{−{d}\theta}{\mathrm{tan}\:\theta\:\left(\mathrm{1}+\mathrm{cos}\:\theta\:\right)} \\ $$$$=−\int\frac{\:\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\theta}{\mathrm{2}}\right)}{\mathrm{2tan}\left(\frac{\theta}{\mathrm{2}}\right)\mathrm{2cos}\:^{\mathrm{2}}…
Question Number 77356 by mathocean1 last updated on 05/Jan/20 $$\mathrm{The}\:\mathrm{plan}\:\mathrm{is}\:\mathrm{provided}\:\mathrm{with}\:\mathrm{an}\: \\ $$$$\mathrm{orthonormal}\:\mathrm{reference}\:\left(\:\mathrm{O}.\mathrm{I}.\mathrm{J}\right). \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{points}\:\mathrm{are}\:\mathrm{given} \\ $$$$\mathrm{A}\left(\mathrm{1},\mathrm{2}\right)\:\mathrm{B}\left(−\mathrm{2},\mathrm{3}\right)\:\mathrm{C}\left(\mathrm{1},\mathrm{9}\right). \\ $$$$\mathrm{We}\:\mathrm{assume}\:\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:\mathrm{O}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{barycenter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point}\:\mathrm{A},\mathrm{B},\mathrm{C}. \\ $$$$\rightarrow\mathrm{O}=\mathrm{bar}\left\{\left(\mathrm{A};\mathrm{3}\right),\left(\mathrm{B};\mathrm{1}\right),\left(\mathrm{C};−\mathrm{1}\right)\right\} \\ $$$$ \\…
Question Number 11813 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/Apr/17 Commented by mrW1 last updated on 01/Apr/17 $${depending}\:{on}\:{the}\:{values}\:{of}\:{a}\:{and}\:{b}, \\ $$$${there}\:{are}\:\mathrm{5}\:{cases}: \\ $$$$\left.\mathrm{1}\right)\:{no}\:{solution} \\ $$$$\left.\mathrm{2}\right)\:{one}\:{solution} \\ $$$$\left.\mathrm{3}\right)\:{two}\:{solutions}…
Question Number 142886 by ZiYangLee last updated on 06/Jun/21 $$\mathrm{Evaluate}\:\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \frac{\mathrm{4}{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:}\:{dx} \\ $$ Answered by Ar Brandon last updated on 06/Jun/21 $$=\int_{\mathrm{0}}…
Question Number 77346 by BK last updated on 05/Jan/20 Commented by BK last updated on 05/Jan/20 $$\mathrm{prove}\:\mathrm{that} \\ $$ Commented by mind is power last…
Question Number 142880 by Dwaipayan Shikari last updated on 06/Jun/21 $$\:{Prove}\:{that}\:\boldsymbol{\phi}\left({n}\right)={n}\underset{{k}} {\prod}\left(\mathrm{1}−\frac{\mathrm{1}}{{p}_{{k}} }\right)\:\:\phi\left({n}\right):{Euler}\:{totient}\:{function} \\ $$ Answered by Snail last updated on 06/Jun/21 $${I}\:{am}\:{considering}\:{that}\:{u}\:{know}\:\phi\left({n}\right)\:{is}\:{multiplicative} \\ $$$${function}\:{i}.{e}\:\phi\left({ab}\right)=\phi\left({a}\right)\phi\left({b}\right)..{where}\:{a}\:{and}\:{b}\:…
Question Number 77347 by key of knowledge last updated on 05/Jan/20 $$\mathrm{if}\:\int\mathrm{sin}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{dx}=\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\int\mathrm{cos}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{dx}=? \\ $$ Commented by mind is power last updated on 05/Jan/20…