Question Number 6935 by FilupSmith last updated on 05/Aug/16 $$\boldsymbol{{v}}=<{x}_{{v}} ,\:{y}_{{v}} > \\ $$$$\boldsymbol{{u}}=<{x}_{{u}} ,\:{y}_{{u}} > \\ $$$$\boldsymbol{{v}}\:\mathrm{and}\:\boldsymbol{{u}}\:\mathrm{have}\:\mathrm{angles}: \\ $$$$\theta_{{v}} =\mathrm{tan}\left(\frac{{y}_{{v}} }{{x}_{{v}} }\right)\:\mathrm{and}\:\theta_{{u}} =\mathrm{tan}\left(\frac{{y}_{{u}} }{{x}_{{u}}…
Question Number 138004 by benjo_mathlover last updated on 09/Apr/21 $$ \\ $$What is the minimum value of x+y+z, subject to the condition xyz = a³?…
Question Number 6932 by FilupSmith last updated on 03/Aug/16 $$\mathrm{If}\:\mathrm{a}\:\mathrm{vector}\:\boldsymbol{{v}}\:\mathrm{exists}\:\mathrm{in}\:{n}\:\mathrm{dimensions}: \\ $$$$\boldsymbol{{v}}\in\mathbb{R}^{{n}} \\ $$$$\mathrm{Can}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{dimension}\left(\mathrm{s}\right)? \\ $$ Commented by nburiburu last updated on 04/Aug/16 $${you}\:{mean}\:{if}\:{v}\in\mathbb{R}^{{n}} \:\Rightarrow{v}\in\mathbb{C}^{{n}}…
Question Number 72466 by Learner-123 last updated on 29/Oct/19 $${Prove}\:{that}\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \int_{−\sqrt{\mathrm{1}−\left({y}−\mathrm{1}\right)^{\mathrm{2}} }} ^{\:\:\mathrm{0}\:} \:{xy}^{\mathrm{2}} {dxdy}\:=\:−\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\boldsymbol{{after}}\:\mathrm{changing}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{to}\:\boldsymbol{\mathrm{polar}}\:\boldsymbol{\mathrm{form}}. \\ $$ Commented by Abdo msup. last…
Question Number 138003 by benjo_mathlover last updated on 09/Apr/21 Answered by EDWIN88 last updated on 09/Apr/21 $${begin}\:{from}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}^{{n}} }{{n}!}\:=\:{e}^{{x}} −\mathrm{1}\:.\:{Taking}\:{derivative} \\ $$$$\Rightarrow\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{nx}^{{n}−\mathrm{1}}…
Question Number 72462 by 20190927 last updated on 29/Oct/19 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{4x}\:}\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} \mathrm{arctan}\left(\mathrm{x}^{\mathrm{5}} \right)} \\ $$ Commented by kaivan.ahmadi last updated on 29/Oct/19 $${lim}_{{x}\rightarrow\mathrm{0}} \frac{\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{4}{x}}\left(\mathrm{1}−\frac{{x}^{\mathrm{4}}…
Question Number 72458 by naka3546 last updated on 29/Oct/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 6923 by Tawakalitu. last updated on 03/Aug/16 $${Find}\:{the}\:{principal}\:{value}\:{of}\:\left(\mathrm{3}\:+\:\mathrm{4}{i}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$ Commented by Yozzii last updated on 03/Aug/16 $$\mathrm{3}+\mathrm{4}{i}=\sqrt{\mathrm{3}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} }{e}^{{itan}^{−\mathrm{1}} \left(\mathrm{4}/\mathrm{3}\right)} =\mathrm{5}{e}^{{itan}^{−\mathrm{1}} \frac{\mathrm{4}}{\mathrm{3}}}…
Question Number 6922 by Tawakalitu. last updated on 02/Aug/16 $${x}^{{y}} \:=\:{y}^{{x}} \\ $$$$ \\ $$$${make}\:{x}\:{the}\:{subject}\:{of}\:{the}\:{formular} \\ $$ Commented by Yozzii last updated on 03/Aug/16 $${x}^{{y}}…
Question Number 137991 by EnterUsername last updated on 08/Apr/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}^{\mathrm{3}} \left({sinx}\right){dx} \\ $$ Answered by Ar Brandon last updated on 08/Apr/21 $$\mathrm{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…