Question Number 135935 by Engr_Jidda last updated on 17/Mar/21 $${If}\:\:{v}={r}^{{m}} \:{where}\:{r}=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:}\:,\:{show}\:{that} \\ $$$$\frac{\partial^{\mathrm{2}} {v}}{\partial{x}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {v}}{\partial{y}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {v}}{\partial{z}^{\mathrm{2}} }={m}\left({m}−\mathrm{1}\right){r}^{{m}−\mathrm{2}} \\ $$ Answered…
Question Number 135929 by Engr_Jidda last updated on 17/Mar/21 $${Verify}\:{that}\:{the}\:{following}\:{functions}\:{satisfies} \\ $$$${the}\:{mean}\:{value}\:{theorem}. \\ $$$$\left(\mathrm{1}\right)\:\:\:{f}\left({x}\right)\:=\frac{{x}}{{x}^{\mathrm{2}} −{x}}\:\:\:{at}\:\left[−\mathrm{2},−\mathrm{1}\right] \\ $$$$\left(\mathrm{2}\right)\:\:{f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}\:\:\:{at}\left[−\mathrm{2},\mathrm{2}\right] \\ $$ Terms of Service Privacy…
Question Number 135930 by Engr_Jidda last updated on 17/Mar/21 $${Given}\:{that}\:{f}\left({x}\right)=\:\mathrm{3}{x}−\mathrm{2}\:{and}\:{g}\left({x}\right)=\frac{{x}}{{x}−\mathrm{1}} \\ $$$${find}\:{the}\:{domain}\:{and}\:{range}\:{of}\:{the}\:{following}. \\ $$$$\left(\mathrm{1}\right)\:{f}^{−\mathrm{1}} \bullet{g}\bullet{g}^{−\mathrm{1}} \bullet{f}\:\:\:\:\:\left(\mathrm{2}\right)\:\left[{f}\left({g}\left({x}\right)\right)\right]^{−\mathrm{1}} \\ $$ Answered by dhgt last updated on 04/May/21…
Question Number 135925 by liberty last updated on 17/Mar/21 $${minimum}\:{value}\:{of}\:\sqrt{\left({x}+\mathrm{6}\right)^{\mathrm{2}} +\mathrm{25}}\:+\sqrt{\left({x}−\mathrm{6}\right)^{\mathrm{2}} +\mathrm{121}} \\ $$$${equal}\:{to}? \\ $$ Answered by john_santu last updated on 17/Mar/21 $$\:{Minimum}\:{value}\:{of}\: \\…
Question Number 4739 by shashi kashyap last updated on 04/Mar/16 Answered by 123456 last updated on 04/Mar/16 $${x}^{\mathrm{2}} −{xy}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} +\mathrm{2}=\mathrm{0} \\ $$$$\left(\mathrm{3}−{x}\right){y}^{\mathrm{2}} =−{x}^{\mathrm{2}} −\mathrm{2}…
Question Number 135785 by Chhing last updated on 16/Mar/21 $$ \\ $$$$\:\:\mathrm{Solve}\:\mathrm{differential}\:\mathrm{equations} \\ $$$$\:\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)\mathrm{y}'+\mathrm{6xy}=\mathrm{lnx} \\ $$$$\:\mathrm{help}\:\mathrm{me} \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 70253 by oyemi kemewari last updated on 02/Oct/19 Commented by mathmax by abdo last updated on 02/Oct/19 $${let}\:{I}\:=\int\:{u}^{\mathrm{2}} \sqrt{{u}^{\mathrm{2}} −\mathrm{2}}{du}\:{changement}\:{u}=\sqrt{\mathrm{2}}{ch}\left({x}\right)\:{give} \\ $$$${I}\:=\int\:\mathrm{2}{ch}^{\mathrm{2}} \left({x}\right)\sqrt{\mathrm{2}}{sh}\left({x}\right)\sqrt{\mathrm{2}}{sh}\left({x}\right){dx}…
Question Number 4486 by Rasheed Soomro last updated on 31/Jan/16 $${f}\left({x}\right)={e}^{{x}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)\:{and}\:{the}\:{domain}\:{D}\left({f}\right)\:{of}\:\:{f} \\ $$$${is}\:{chosen}\:{appropriately},\:{find}\:\frac{{d}}{{dx}}{f}\left({x}\right)\:\:{at}\: \\ $$$${any}\:{point}\:{x}\:{in}\:{D}\left({f}\right)\:. \\ $$ Answered by Yozzii last updated on…
Question Number 4487 by Rasheed Soomro last updated on 31/Jan/16 $${If}\:\:{y}^{\mathrm{2}} +\mathrm{3}{uy}−\mathrm{5}{u}^{\mathrm{2}} =\mathrm{2}\:,\:\:\mathrm{2}{t}^{\mathrm{2}} −\mathrm{2}{tu}−\mathrm{3}{u}^{\mathrm{2}} −\mathrm{1}=\mathrm{0}\: \\ $$$${and}\:\mathrm{5}{x}^{\mathrm{2}} +\mathrm{4}{xt}−{t}^{\mathrm{2}} =\mathrm{0}\:,{find}\:\:\frac{{dy}}{{dx}}\:\:{and}\:\:\:\frac{{du}}{{dt}}\:. \\ $$ Answered by Yozzii last…
Question Number 4363 by Rasheed Soomro last updated on 13/Jan/16 $${If}\:\:\underset{{x}\rightarrow{a}} {{lim}}\:\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}\:{exists}\:{and}\:\underset{{x}\rightarrow{a}} {{lim}}\:{g}\left({x}\right)=\mathrm{0}, \\ $$$${then}\:{show}\:{that} \\ $$$$\underset{{x}\rightarrow{a}} {{lim}}\:{f}\left({x}\right)=\mathrm{0}. \\ $$ Answered by Yozzii last updated…