Question Number 20291 by tammi last updated on 25/Aug/17 $$\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\:{dx}} \\ $$ Answered by $@ty@m last updated on 25/Aug/17 $$=\int\frac{\mathrm{1}−{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$$$=\int\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{−\mathrm{2}{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}…
Question Number 151360 by talminator2856791 last updated on 20/Aug/21 $$\: \\ $$$$\:\:\mathrm{find}\:\mathrm{max}\left(\Re\left(\mathrm{I}\right)+\Im\left(\mathrm{I}\right)\right)\:\mathrm{for}\:\mathrm{the}\:\mathrm{integral} \\ $$$$\:\:\mathrm{I}\:=\:\int_{{z}} ^{\:{z}+\mathrm{1}} \:\mathrm{cos}\left(\mathrm{cos}\left(\mathrm{cos}\left({x}^{\mathrm{cos}\left(\mathrm{cos}\left(\mathrm{cos}\left({x}\right)\right)\right)} \right)\right)\right){dx} \\ $$$$\:\:{z}\:\in\:\mathbb{R} \\ $$$$\: \\ $$ Terms of…
Question Number 151357 by mathdanisur last updated on 20/Aug/21 Commented by mr W last updated on 20/Aug/21 $${check}\:{the}\:{question}\:{please}! \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}{a}_{{k}} \geqslant\mathrm{100}\:{and}\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}{a}_{{k}}…
Question Number 85822 by jagoll last updated on 25/Mar/20 $$\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\: \\ $$$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{3}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{5}}\:=\:\mathrm{0}\: \\ $$ Commented by jagoll last updated on 25/Mar/20 $$\mathrm{thank}\:\mathrm{mr}\: \\ $$ Answered…
Question Number 20281 by ajfour last updated on 25/Aug/17 $${Compute}\:{the}\:{volume}\:{bounded}\:{by} \\ $$$${the}\:{surfaces}:\:{y}={x}^{\mathrm{2}} ,\:{x}={y}^{\mathrm{2}} ,\:{z}=\mathrm{0}, \\ $$$${z}=\mathrm{12}+{y}−{x}^{\mathrm{2}} .\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:{Ans}.\:\:\:\:\frac{\mathrm{549}}{\mathrm{144}}\right] \\ $$ Terms of Service Privacy…
Question Number 85817 by jagoll last updated on 25/Mar/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{in}\: \\ $$$$\mathrm{the}\:\mathrm{expansion}\:\left[\:\left(\mathrm{1}−\mathrm{x}\right)\left(\mathrm{1}+\mathrm{2x}\right)\right]^{\mathrm{6}} \\ $$ Answered by john santu last updated on 25/Mar/20 $$\left(\mathrm{1}+{x}−\mathrm{2}{x}^{\mathrm{2}} \right)^{\mathrm{6}\:\:}…
Question Number 20279 by ajfour last updated on 25/Aug/17 $${Determine}\:{a}\:{relation}\:{between}\:\:{the} \\ $$$${coefficients}\:\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}},\:\boldsymbol{{d}}\:{such}\:{that}\:{the} \\ $$$${equation}:\:\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${has}\:{three}\:{real}\:{roots}\:\left({with}\:{a}\:{pair}\right. \\ $$$$\left.{of}\:{double}\:{roots}\right). \\ $$ Terms of Service…
Question Number 151351 by mathdanisur last updated on 20/Aug/21 Answered by dumitrel last updated on 20/Aug/21 $$\:\lambda\sqrt{\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{2}}}+\frac{\mathrm{2}{ab}}{{a}+{b}}\geqslant\frac{\lambda+\mathrm{1}}{\mathrm{2}}\left({a}+{b}\right) \\ $$$${if}\:{a}={b}\:{true} \\ $$$${suppose}\:{a}<{b}\:;\frac{{a}}{{b}}={t}\in\left(\mathrm{0};\mathrm{1}\right) \\ $$$$\Leftrightarrow\lambda\sqrt{\frac{{t}^{\mathrm{2}}…
Question Number 151350 by mathdanisur last updated on 20/Aug/21 Commented by dumitrel last updated on 20/Aug/21 $$\mathrm{0}\leqslant\lambda\leqslant\mathrm{8}\:{sau}\:\mathrm{0}\leqslant\lambda\leqslant\mathrm{5}\:????? \\ $$$${p}^{\mathrm{2}} \geqslant\mathrm{3}{q}\Rightarrow{q}\leqslant\mathrm{3} \\ $$$$\left({a}+{b}+{c}\right)^{\mathrm{3}} ={a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}}…
Question Number 85813 by jagoll last updated on 25/Mar/20 $$\int\:\mathrm{x}^{\mathrm{2}} \:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:? \\ $$ Commented by jagoll last updated on 25/Mar/20 $$\int\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\:\left(\mathrm{2x}\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\right)\:\mathrm{dx}\:=\: \\ $$$$\int\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}}…