Question Number 78073 by jagoll last updated on 14/Jan/20 $${anyone}\:{have}\:{Lambert}\:{W}\:{function} \\ $$$${formula}.\:{please}\:{post}\:{in}\:{forum} \\ $$ Commented by mr W last updated on 14/Jan/20 $${google},\:{wikipedia},\:{etc}. \\ $$…
Question Number 12535 by tawa last updated on 24/Apr/17 $$\mathrm{Use}\:\mathrm{the}\:\mathrm{reduction}\:\mathrm{formular}. \\ $$$$\mathrm{I}_{\mathrm{n}} \:=\:\int\mathrm{sin}^{\mathrm{n}} \left(\mathrm{x}\right)\:\mathrm{dx}\:=\:−\frac{\mathrm{1}}{\mathrm{n}}\:\mathrm{sin}^{\mathrm{n}\:−\:\mathrm{1}} \left(\mathrm{x}\right)\mathrm{cos}\left(\mathrm{x}\right)\:+\:\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}}\mathrm{I}_{\mathrm{n}} \:−\:\mathrm{2}\:,\:\mathrm{to}\:\mathrm{evaluate}\: \\ $$$$\mathrm{I}_{\mathrm{n}\:} =\:\int\mathrm{sin}^{\mathrm{6}} \left(\mathrm{x}\right)\:\mathrm{dx} \\ $$ Answered by mrW1…
Question Number 12534 by JAZAR last updated on 24/Apr/17 $${please}\:{help}\:{me}\:.{How}\:{can}\:{resolve}\:{this}\:{system}? \\ $$$$\left\{_{\left(\mathrm{1}+\sqrt{\mathrm{2}}\right){x}+{y}=\mathrm{1}} ^{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}} \right. \\ $$ Answered by geovane10math last updated on 25/Apr/17…
Question Number 12533 by tawa last updated on 24/Apr/17 $$\mathrm{compute} \\ $$$$\int\mathrm{sec}^{\mathrm{5}} \left(\mathrm{x}\right)\:\mathrm{tan}^{\mathrm{3}} \left(\mathrm{x}\right)\:\mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 25/Apr/17 $${I}=\int{sec}^{\mathrm{5}} \left({x}\right){tan}^{\mathrm{3}}…
Question Number 143606 by bobhans last updated on 16/Jun/21 Answered by TheHoneyCat last updated on 16/Jun/21 $${f}\:\mathrm{surjective}\:\Leftrightarrow\:\:\left[\mathrm{1},\:+\infty\left[\subset{f}\left(\mathbb{R}\right)\right.\right. \\ $$$$ \\ $$$$\mathrm{knowing}\:\mathrm{that}\:{f}\in\mathscr{C}^{\mathrm{0}} \left(\mathbb{R},\left[\mathrm{1},+\infty\left[\right)\right.\right. \\ $$$$\mathrm{and}\:\mathrm{that}\:\:{f}\left({x}\right)\underset{{x}\rightarrow\mp\infty} {\rightarrow}+\infty…
Question Number 12532 by tawa last updated on 24/Apr/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\::\:\:\mathrm{p} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{2x}\right)\:+\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{3x}\right)\:=\:\frac{\pi}{\mathrm{4}} \\ $$ Answered by mrW1 last updated on 25/Apr/17 $$\mathrm{tan}\:\left[\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{2x}\right)\:+\:\mathrm{tan}^{−\mathrm{1}}…
Question Number 143603 by mnjuly1970 last updated on 16/Jun/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…..{Calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\Omega:=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{{k}} \left(\mathrm{1}+{n}\right)}\:\:\:\left({k}\geqslant\:\mathrm{2}\right)\:…… \\ $$ Answered by Dwaipayan Shikari last updated on 16/Jun/21…
Question Number 143602 by meetbhavsar25 last updated on 16/Jun/21 Commented by TheHoneyCat last updated on 16/Jun/21 $$\mathrm{Are}\:\mathrm{you}\:\mathrm{asking}\:\mathrm{for}\:\underset{{a}\in\mathbb{C}} {\prod}{g}\left({a}\right)^{\mathrm{val}_{{f}} \left({a}\right)} \\ $$$$ \\ $$$$\mathrm{or}\:{z}\:\mathrm{such}\:\mathrm{that} \\ $$$$\forall\left({a}_{{i}}…
Question Number 143597 by Videz last updated on 16/Jun/21 $${s}\:=\:{ut}\:+\:\frac{\mathrm{1}}{\mathrm{2}}{at}^{\mathrm{2}} \:\:\Rightarrow\:\:{t}^{\mathrm{2}} \:+\:\mathrm{2}\frac{{u}}{{a}}{t}\:−\:\mathrm{2}\frac{{s}}{{a}}\:=\:\mathrm{0} \\ $$$${by}\:{the}\:{use}\:{of}\:{quadratic}\:{formula} \\ $$$${t}\:=\:\frac{−\frac{\mathrm{2}{u}}{{a}}\:\pm\:\sqrt{\frac{\mathrm{4}{u}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\:\mathrm{4}{s}}}{\mathrm{2}} \\ $$$${t}\:=\:−\frac{{u}}{{a}}\:\:\pm\:\:\sqrt{\frac{{u}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\:{s}} \\ $$$${Victor}\:\:{Francis} \\…
Question Number 143596 by ZiYangLee last updated on 16/Jun/21 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{series} \\ $$$$\frac{{x}}{\mathrm{3}^{} }+\frac{{y}}{\mathrm{3}^{\mathrm{2}} }+\frac{{x}}{\mathrm{3}^{\mathrm{3}} }+\frac{{y}}{\mathrm{3}^{\mathrm{4}} }+\ldots+\frac{{x}}{\mathrm{3}^{{n}−\mathrm{1}} }+\frac{{y}}{\mathrm{3}^{{n}} }=\mathrm{8},\:{x},{y}\in\mathbb{R}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{3}{x}+{y}. \\ $$ Answered by bobhans…