Question Number 91812 by niroj last updated on 03/May/20 $$\:\mathrm{Solve}\:\mathrm{clairaut}'\mathrm{s}\:\mathrm{equation}\:\mathrm{and}\:\mathrm{find} \\ $$$$\:\mathrm{general}\:\mathrm{and}\:\mathrm{singular}\:\mathrm{solution}: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{y}=\mathrm{px}+\mathrm{p}^{\mathrm{n}} \\ $$$$\:\left(\mathrm{ii}\right)\:\left(\mathrm{y}+\mathrm{1}\right)\mathrm{p}−\mathrm{xp}^{\mathrm{2}} +\mathrm{2}=\mathrm{0} \\ $$$$ \\ $$$$ \\ $$ Commented by…
Question Number 157278 by mnjuly1970 last updated on 21/Oct/21 Answered by mindispower last updated on 21/Oct/21 $${tanh}^{−} \left({x}\right)=\underset{{m}\geqslant\mathrm{0}} {\sum}\frac{{x}^{\mathrm{2}{m}+\mathrm{1}} }{\mathrm{2}{m}+\mathrm{1}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left(\mathrm{1}−\sqrt{{x}}\right){tanh}^{−} \left(\sqrt{{x}}\right)}{{x}}{dx}…
Question Number 157247 by john_santu last updated on 21/Oct/21 $${F}\left({x},{y}\right)={x}^{\mathrm{2}} −\mathrm{2}{xy}+\mathrm{6}{y}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{2}{y}+\mathrm{45} \\ $$$${find}\:{x}\:\&{y}\:{such}\:{that}\:{F}\left({x},{y}\right)\:{minimum} \\ $$ Answered by FongXD last updated on 21/Oct/21 $$\mathrm{Given}:\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{2xy}+\mathrm{6y}^{\mathrm{2}}…
Question Number 26126 by NECx last updated on 20/Dec/17 $${using}\:\mathrm{1}{st}\:{principle}\:{find}\:{the} \\ $$$${derivative}\:{of} \\ $$$$\:\:\:\:\:\:\:\:{y}={x}^{{x}} \\ $$ Commented by abdo imad last updated on 20/Dec/17 $${answer}\:{to}\:{question}\:\:{ew}\:{have}\:{y}=\:{e}^{{xlnx}}…
Question Number 157169 by cortano last updated on 20/Oct/21 Answered by mr W last updated on 20/Oct/21 $${x}={r}\:\mathrm{cos}\:\theta \\ $$$${y}={r}\:\mathrm{sin}\:\theta \\ $$$${r}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \:\theta+\mathrm{2}{r}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}}…
Question Number 91635 by john santu last updated on 02/May/20 $${given}\:{f}\left({x}\right)=\mathrm{log}_{\mathrm{10}} \left({x}\right)\:{and}\:\mathrm{log}_{\mathrm{10}} \left(\mathrm{102}\right)\approx\mathrm{2}.\mathrm{0086} \\ $$$$,\:{which}\:{is}\:{closest}\:{to}\:{f}\:'\left(\mathrm{100}\right)? \\ $$$${A}.\:\mathrm{0}.\mathrm{0043}\:\:\:\:\:\:{B}.\mathrm{0}.\mathrm{0086} \\ $$$${C}.\:\mathrm{0}.\mathrm{01}\:\:\:\:\:\:\:\:\:\:{E}.\:\mathrm{1}.\mathrm{0043} \\ $$ Commented by mr W…
Question Number 26073 by gopikrishnan005@gmail.com last updated on 19/Dec/17 $$ \\ $$$${solve}\:{the}\:{differential}\:{equation}\left({D}^{\mathrm{2}} +\mathrm{2}{D}+\mathrm{1}\right){y}={x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1} \\ $$ Commented by gopikrishnan005@gmail.com last updated on 20/Dec/17 $${pls}\:{explain} \\…
Question Number 157116 by cortano last updated on 20/Oct/21 $$\:{max}\:\wedge\:{min}\:{of}\:{f}\left({x}\right)\:=\sqrt{{x}}\:+\mathrm{4}\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{2}}} \\ $$ Commented by cortano last updated on 20/Oct/21 $${without}\:{derivative} \\ $$ Commented by mr…
Question Number 91460 by M±th+et+s last updated on 30/Apr/20 $${one}\:{of}\:{the}\:{conditions}\:{of}\:{the}\:{inflection} \\ $$$${point}\:{is}\:{inflection}\:{tangent}. \\ $$$${what}\:{is}\:{inflection}\:{tangent}? \\ $$ Answered by MJS last updated on 01/May/20 $$\mathrm{it}'\mathrm{s}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{in}\:\mathrm{the}\:\mathrm{inflection}\:\mathrm{point}\:\mathrm{which} \\…
Question Number 25845 by NECx last updated on 15/Dec/17 $${using}\:{the}\:\mathrm{1}{st}\:{principle}\:{find}\:{the} \\ $$$${derivative}\:{of}\: \\ $$$$\:\:\:\:\:{y}=\left({ax}+{b}\right)^{{n}} \\ $$ Answered by ajfour last updated on 15/Dec/17 $$\frac{{dy}}{{dx}}=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({ax}+{ah}+{b}\right)^{{n}}…