Question Number 63378 by minh2001 last updated on 03/Jul/19 $$\underset{\mathrm{2}} {\overset{{x}} {\int}}\frac{\mathrm{1}}{{x}}{dx}=\mathrm{2}{ln}\left(\mathrm{3}\right)−{ln}\left(\mathrm{2}\right) \\ $$$${please}\:{help}\:{me}\:{to}\:{solve}\:{for}\:{x} \\ $$ Answered by MJS last updated on 03/Jul/19 $$\mathrm{the}\:\mathrm{borders}\:\mathrm{must}\:\mathrm{be}\:\mathrm{independent}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{variable} \\…
Question Number 63301 by Rio Michael last updated on 02/Jul/19 $${find}\:\frac{{dy}}{{dx}}\:{if}\:\:{x}\left({x}\:+{y}\right)\:=\:{y}^{\mathrm{2}} \\ $$ Commented by kaivan.ahmadi last updated on 02/Jul/19 $${f}\left({x},{y}\right)={x}^{\mathrm{2}} +{xy}−{y}^{\mathrm{2}} =\mathrm{0} \\ $$$$\frac{{dy}}{{dx}}=−\frac{{f}'_{{x}}…
Question Number 128751 by bemath last updated on 10/Jan/21 $$\mathrm{Find}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\mid\mathrm{x}\mid\:\sqrt{\mathrm{16}−\mathrm{y}^{\mathrm{2}} }\:+\:\mid\mathrm{y}\mid\:\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\:\mathrm{for}\:\mathrm{all}\:\mathrm{real}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}. \\ $$$$ \\ $$ Answered by mr W last updated on…
Question Number 63152 by Rio Michael last updated on 29/Jun/19 $${The}\:{Variables}\:{x}\:{and}\:{y}\:{satisfy}\:{the}\:{differential}\:{equation}\: \\ $$$$\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−{x}\frac{{dy}}{{dx}}\:+\:{y}\:=\:{x}^{\mathrm{2}} \:\:{use}\:{the}\:{approximations} \\ $$$$\:\:\:\left(\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\right)_{{n}} \approx\:\frac{{y}_{{n}+\mathrm{1}} −\mathrm{2}{y}_{{n}} +{y}_{{n}−\mathrm{1}} }{{h}^{\mathrm{2}\:} }\:{and}\:\:\left(\frac{{dy}}{{dx}}\right)\approx\frac{{y}_{{n}+\mathrm{1}}…
Question Number 63128 by Tawa1 last updated on 29/Jun/19 $$\mathrm{Examine}\:\mathrm{the}\:\mathrm{following}\:\mathrm{function}\:\mathrm{for}\:\mathrm{extreme}\:\mathrm{value} \\ $$$$\:\:\:\:\mathrm{f}\left(\mathrm{x},\:\mathrm{y}\right)\:\:=\:\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:−\:\mathrm{2x}^{\mathrm{3}} \:+\:\mathrm{4xy}\:−\:\mathrm{2y}^{\mathrm{2}} \\ $$ Commented by Hope last updated on 29/Jun/19 Commented…
Question Number 63015 by ajfour last updated on 27/Jun/19 $${f}\left({x},{y},{z}\right)=\:{x}\left({p}+{z}\right)+{y}\left({p}−{z}\right) \\ $$$$\:\:\:\:+\frac{\mathrm{4}{x}^{\mathrm{3}} }{{p}+{z}}+\frac{\mathrm{4}{y}^{\mathrm{3}} }{{p}−{z}}+\mathrm{4}\left({x}+{y}\right)^{\mathrm{2}} \left({y}−{x}\right) \\ $$$$\forall\:\:{p}\left({x},{y}\right)={c}+\left({x}−{y}\right)\sqrt{\mathrm{1}+\left({x}+{y}\right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right) \\ $$$${Determine}\:{x},{y},{z}\:{such}\:{that}\:{f}\:{is} \\…
Question Number 128521 by bramlexs22 last updated on 08/Jan/21 $$\mathrm{A}\:\mathrm{curve}\:\mathrm{has}\:\mathrm{equation}\:\mathrm{y}\:=\:\left(\mathrm{2}−\sqrt{\mathrm{x}}\:\right)^{\mathrm{4}} \\ $$$$\mathrm{The}\:\mathrm{normal}\:\mathrm{at}\:\mathrm{point}\:\mathrm{P}\left(\mathrm{1},\mathrm{1}\right)\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{normal}\:\mathrm{at}\:\mathrm{point}\:\mathrm{Q}\left(\mathrm{9},\mathrm{1}\right)\:\mathrm{intersect} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\mathrm{R}.\:\mathrm{What}\:\mathrm{are}\:\mathrm{coordinates} \\ $$$$\mathrm{at}\:\mathrm{point}\:\mathrm{R}? \\ $$ Answered by mr W last…
Question Number 128489 by mnjuly1970 last updated on 07/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{calculus}\:\:\:\left(\mathrm{2}\right)\:… \\ $$$$\:\:\:\:{evaluate}\:::\:\:\: \\ $$$$\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{2}^{{n}} }{\mathrm{1}+\mathrm{2}^{\mathrm{2}^{{n}} } }\:\right)=? \\ $$$$ \\ $$ Answered by…
Question Number 62869 by aliesam last updated on 26/Jun/19 $${y}\frac{{dy}}{{dx}}\:−\:\frac{{y}}{\frac{{dy}}{{dx}}}\:=\:\mathrm{2}{a} \\ $$$$ \\ $$$${a}\:{is}\:{a}\:{real}\:{number} \\ $$ Answered by Hope last updated on 26/Jun/19 $${y}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} −{y}=\mathrm{2}{a}\left(\frac{{dy}}{{dx}}\right)…
Question Number 62809 by mathmax by abdo last updated on 25/Jun/19 $${let}\:{f}\left({x}\right)\:=\:{arctan}\left({nx}\right)\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$ Commented by mathmax by abdo…