Question Number 8695 by vuckintv last updated on 22/Oct/16 $${solving}\:{for}\:{B}? \\ $$$${U}_{{b}} \:=\:{U}_{{s}} \:−\:\frac{\mathrm{2}}{{n}+\mathrm{1}}\left(\frac{\rho×{g}×{sin}\alpha}{{B}}\right)^{{n}} {H}^{{n}+\mathrm{1}} \\ $$ Answered by FilupSmith last updated on 22/Oct/16 $${U}_{{b}}…
Question Number 74231 by necxxx last updated on 20/Nov/19 Commented by necxxx last updated on 20/Nov/19 Commented by necxxx last updated on 20/Nov/19 $${here}\:{was}\:{a}\:{step}\:{taken}\:{though}\:{not}\:{so} \\…
Question Number 139766 by mohammad17 last updated on 01/May/21 $${lim}_{{x}\rightarrow\mathrm{0}} \left(\frac{\sqrt{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}}{\mathrm{1}−{cos}\left({x}\right)}\right) \\ $$ Answered by bramlexs22 last updated on 01/May/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}−\left(\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}\right)}}{\mathrm{1}−\mathrm{cos}\:\mathrm{x}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 74226 by MASANJAJ last updated on 20/Nov/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8691 by FilupSmith last updated on 22/Oct/16 $$\int_{\mathrm{0}} ^{\:\infty} {x}^{−\mathrm{ln}\left({x}\right)} {dx} \\ $$ Commented by FilupSmith last updated on 22/Oct/16 $${x}^{−\mathrm{ln}\left({x}\right)} ={e}^{−\mathrm{ln}\left({x}\right)\mathrm{ln}\left({x}\right)} ={e}^{−\mathrm{ln}^{\mathrm{2}}…
Question Number 74224 by mathmax by abdo last updated on 20/Nov/19 $${find}\:\int\:\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx}\:\:{and} \\ $$$$\int\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} {sin}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx} \\ $$ Commented by mathmax by abdo…
Question Number 139762 by mathdanisur last updated on 01/May/21 $${x};{y};{z}>\mathrm{0},\:\gamma\geqslant\mathrm{0},\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} +{xyz}=\mathrm{4} \\ $$$${proof}:\:\left({x}+{y}+{z}\right)^{\mathrm{3}} +\gamma\left({x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} \right)\geqslant\mathrm{27}+\mathrm{3}\gamma \\ $$ Answered by mindispower last…
Question Number 74225 by mathmax by abdo last updated on 20/Nov/19 $${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} −\left(\mathrm{1}−{jx}\right)^{{n}} \:\:{with}\:{j}={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{p}\left({x}\right)\:{and}\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{p}\left({x}\right)} \\ $$ Answered by mind is power…
Question Number 139756 by cherokeesay last updated on 01/May/21 Answered by mr W last updated on 01/May/21 Commented by mr W last updated on 01/May/21…
Question Number 74223 by mathmax by abdo last updated on 20/Nov/19 $${calculate}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}{dx}\:\:\:{and}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\:\sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}} \\ $$$${with}\:\:\mid{a}\mid<\mathrm{2} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}{dx}\:{and}\:\int_{\mathrm{0}}…