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…
Question Number 128279 by liberty last updated on 06/Jan/21 $$\:\:\Theta\:=\:\int_{\mathrm{1}} ^{\:\mathrm{e}} \:\frac{{dx}}{{x}.\sqrt[{\mathrm{3}}]{\mathrm{ln}\:{x}}}\:?\: \\ $$ Answered by john_santu last updated on 06/Jan/21 $$\:{let}\:\sqrt[{\mathrm{3}\:}]{\mathrm{ln}\:{x}}\:=\:{w}\:\Rightarrow\:\frac{{dx}}{{x}}\:=\:\mathrm{3}{w}^{\mathrm{2}} \:{dw} \\ $$$$\:\Theta\:=\:\int_{\mathrm{0}}…
Question Number 128225 by mnjuly1970 last updated on 05/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\:\phi\:=\:\int_{\mathrm{0}} ^{\:\pi} \frac{{tan}^{−\mathrm{1}} \left({tan}^{\mathrm{2}} \left({x}\right)\right)}{{tan}^{\mathrm{2}} \left({x}\right.}\:{dx}\overset{???} {=}\pi\left(\sqrt{\mathrm{2}}\:−\frac{\pi}{\mathrm{4}}\right) \\ $$$$ \\ $$ Answered…
Question Number 62679 by ajfour last updated on 24/Jun/19 $${Let}\:{f}\:{be}\:{defined}\:{in}\:{the}\:{neighborhood} \\ $$$${of}\:{x}\:{and}\:{that}\:{f}\:''\left({x}\right)\:{exists}. \\ $$$${Prove}\:{that}\:\: \\ $$$$\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{f}\left({x}+{h}\right)+{f}\left({x}−{h}\right)−\mathrm{2}{f}\left({x}\right)}{{h}^{\mathrm{2}} }={f}\:''\left({x}\right)\:. \\ $$ Commented by kaivan.ahmadi last updated…
Question Number 128156 by DomaPeti last updated on 04/Jan/21 $${f}\left({x}\right)''=\frac{\mathrm{1}}{{f}\left({x}\right)^{\mathrm{2}} }\:\:\:\:\: \\ $$$${f}\left({x}\right)=? \\ $$ Answered by mr W last updated on 05/Jan/21 $${let}\:{y}'={u} \\…