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…
Question Number 135342 by Algoritm last updated on 12/Mar/21 Commented by Algoritm last updated on 12/Mar/21 $$\frac{\mathrm{d}^{\mathrm{n}} \left(\mathrm{y}\right)}{\mathrm{dx}^{\mathrm{n}} }=? \\ $$ Answered by Ñï= last…
Question Number 135313 by bobhans last updated on 12/Mar/21 $${Given}\:{f}\left({x}\right)\:=\:\mathrm{5}{x}+\mathrm{cos}\:\left(\mathrm{3}{x}\right) \\ $$$${Find}\:{the}\:{value}\:{of}\:\frac{{d}}{{dx}}\:\left[{f}^{−\mathrm{1}} \left(\mathrm{1}\right)\right] \\ $$ Answered by liberty last updated on 12/Mar/21 $$\left(\mathrm{1}\right){f}\left(\mathrm{0}\right)=\mathrm{1}\Leftrightarrow{f}^{−\mathrm{1}} \left(\mathrm{1}\right)=\mathrm{0} \\…
Question Number 135309 by mnjuly1970 last updated on 12/Mar/21 $$\:\:\:\:\:\:\:\:\:\:….\:\:\mathscr{N}{ice}\:\:\:\:\mathscr{C}{alculus}\:…. \\ $$$$\:\:\:\:\:\:\:\:{prove}\:\:{that}\:::: \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({ksin}\alpha\right){x}}{\:\sqrt{{x}}}{dx}=\sqrt{\frac{\pi}{{k}}}\:{sin}\left(\frac{\alpha}{\mathrm{2}}\right)… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered by mathmax…
Question Number 135308 by bobhans last updated on 12/Mar/21 Commented by mr W last updated on 12/Mar/21 $${at}\:{t}=\mathrm{3}\:{s},\:{the}\:{height}\:{is}\:\mathrm{71}.\mathrm{65}{m} \\ $$$${at}\:{t}=\mathrm{7}.\mathrm{8009}{s},\:{the}\:{ball}\:{hits}\:{the}\:{ground} \\ $$$${max}.\:{height}\:{is}\:\mathrm{75}.\mathrm{4235}{m} \\ $$$${in}\:\mathrm{6}.\mathrm{1554}−\mathrm{1}.\mathrm{5997}=\mathrm{4}.\mathrm{5557}{s}\:{the}\:{ball} \\…
Question Number 135252 by mnjuly1970 last updated on 11/Mar/21 $$\:\:\:\:\:\:\:\:\:….{advanced}\:\:\:\:{calculus}…. \\ $$$$\:\:\:\:{first}\:{prove}\:{that}::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}_{\mathrm{1}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx}=\frac{−\mathrm{5}}{\mathrm{8}}\:\zeta\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:{then}\:{conclude}\:{that}:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}_{\mathrm{2}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)}{{x}}{dx}=\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{4}}…