Question Number 71142 by mathmax by abdo last updated on 12/Oct/19 $${find}\:\int\sqrt{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx} \\ $$ Commented by MJS last updated on 12/Oct/19 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this} \\ $$ Terms…
Question Number 71143 by mathmax by abdo last updated on 12/Oct/19 $${let}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\:{calculate}\:{A}_{{n}} \:{interms}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$ Commented by mathmax by…
Question Number 136679 by mnjuly1970 last updated on 24/Mar/21 $$\:\:\:\:\:\:\:\:\:{arcsin}\sqrt{{x}}\:+{arcsin}\left(\sqrt{\mathrm{1}−{x}}\:\right)={t} \\ $$$$\:\:\:\:\:\:{sin}\left(\alpha\right)=\sqrt{{x}}\:\:\:\:{sin}\left(\beta\right)=\sqrt{\mathrm{1}−{x}}\: \\ $$$$\:\:\:\:\alpha+\beta={t} \\ $$$$\:\:\:\:{sin}\left(\alpha\right){cos}\left(\beta\right)+{cos}\left(\alpha\right){sin}\left(\beta\right)={sin}\left({t}\right) \\ $$$$\:\:\sqrt{{x}\:}\:.\sqrt{\mathrm{1}−\mathrm{1}+{x}}\:+\sqrt{\mathrm{1}−{x}}\:.\sqrt{\mathrm{1}−{x}}\: \\ $$$$={x}+\mathrm{1}−{x}=\mathrm{1} \\ $$$$\:\:\:{t}=\frac{\pi}{\mathrm{2}}… \\ $$$$\:\:\: \\…
Question Number 71141 by Mr. K last updated on 12/Oct/19 $$\left(\mathrm{2}{x}\right)^{{x}} =\frac{\mathrm{1}}{\mathrm{16}} \\ $$ Commented by mr W last updated on 12/Oct/19 $$\left(\mathrm{2}{x}\right)^{{x}} =\sqrt{\left(\mathrm{2}{x}\right)^{\mathrm{2}{x}} }=\sqrt{{t}^{{t}}…
Question Number 5603 by sanusihammed last updated on 22/May/16 $${Prove}\:{the}\:{identity} \\ $$$$ \\ $$$${log}_{\frac{{a}}{{b}}} {x}\:\:=\:\:\frac{{log}_{{a}} {x}\:{log}_{{b}} {x}}{{log}_{{b}} {x}\:−\:{log}_{{a}} {x}} \\ $$$$ \\ $$$${From}\:{the}\:{Right}\:{hand}\:{side}\: \\ $$$$…
Question Number 71134 by Mr. K last updated on 11/Oct/19 $${if}\:{a},\:{b}\:{and}\:{c}\:{are}\:{positive},\:{find}: \\ $$$$\left(\frac{{a}}{{b}}\right)^{{log}_{\mathrm{10}} {c}} ×\left(\frac{{b}}{{c}}\right)^{{log}_{\mathrm{10}} {a}} ×\left(\frac{{c}}{{a}}\right)^{{log}_{\mathrm{10}} {b}} \\ $$$$ \\ $$ Answered by MJS…
Question Number 5597 by Rasheed Soomro last updated on 21/May/16 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{degree}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{2}^{\mathrm{x}} \:? \\ $$$$\mathrm{Is}\:\mathrm{its}\:\mathrm{graph}\:\mathrm{parabola}? \\ $$ Commented by Rasheed Soomro last updated on 22/May/16…
Question Number 136670 by rexford last updated on 24/Mar/21 Answered by Dwaipayan Shikari last updated on 24/Mar/21 $$\mathrm{0} \\ $$ Answered by MJS_new last updated…
Question Number 136667 by mathlove last updated on 24/Mar/21 $${if}\:\:\:\:\:\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c}\:\:\:\:\:\:{and}\:\:\:{f}\left(\mathrm{5}\right)=−\mathrm{3}{f}\left(\mathrm{2}\right) \\ $$$${an}\:{intersiction}\:\:{point}\:\:\left(−\mathrm{4},\mathrm{0}\right) \\ $$$${an}\:{the}\:\:{X}-{axis}\:\:\:\:\:{faind}\:{another}\:{point}\: \\ $$$${the}\:{X}-{axis} \\ $$$$ \\ $$ Answered by MJS_new last…
Question Number 5593 by sanusihammed last updated on 21/May/16 $${Find}\:{the}\:{limit} \\ $$$$ \\ $$$${limit}\:\:\:\:\:\:\:\left[\mathrm{1}\:+\:{mt}\right]^{\frac{\mathrm{2}}{{t}}} \\ $$$${t}\:\rightarrow\infty \\ $$ Answered by FilupSmith last updated on 21/May/16…