Question Number 204499 by DeArtist last updated on 19/Feb/24 $$\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{directional}\:\mathrm{derivative}\:\mathrm{of}\: \\ $$$${F}\left({x},{y},{z}\right)\:=\:\mathrm{2}{xy}−{z}^{\mathrm{2}} \:\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},−\mathrm{1},\mathrm{1}\right)\:\mathrm{in} \\ $$$$\mathrm{a}\:\mathrm{direction}\:\mathrm{towards}\:\left(\mathrm{3},\mathrm{1},−\mathrm{1}\right)\: \\ $$$$\mathrm{in}\:\mathrm{what}\:\mathrm{direction}\:\mathrm{is}\:\mathrm{the}\:\mathrm{directional}\:\mathrm{derivative} \\ $$$$\mathrm{maximum}?\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{this}\:\mathrm{maximum}? \\ $$ Answered by TonyCWX08 last…
Question Number 204477 by universe last updated on 18/Feb/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{2n}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\right)^{\mathrm{n}} =? \\ $$ Answered by witcher3 last updated on 18/Feb/24…
Question Number 204478 by a.lgnaoui last updated on 18/Feb/24 $$\mathrm{soit}\:\boldsymbol{\mathrm{f}}:\:\:\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}^{\mathrm{3}} \:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}},\boldsymbol{\mathrm{z}}\right)=\left(\mathrm{x}+\mathrm{y},\mathrm{2x}−\mathrm{y},\mathrm{x}+\mathrm{z}\right) \\ $$$$\bullet\mathrm{1}\:\:\mathrm{Ecrire}\:\mathrm{la}\:\mathrm{matrice}\:\mathrm{M}\:\mathrm{de}\:\mathrm{cette}\:\mathrm{application} \\ $$$$\:\:\:\mathrm{dans}\:\mathrm{la}\:\mathrm{base}\:\mathrm{canonique}\:{B}\:\mathrm{de}\:\:\mathbb{R}^{\mathrm{3}} \: \\ $$$$\bullet\mathrm{2}\:\:\mathrm{Calculer}\:\boldsymbol{\mathrm{f}}\left(\mathrm{1},\mathrm{2},\mathrm{3}\right)\mathrm{de}\:\mathrm{2}\:\mathrm{manieres}\:\mathrm{differentes} \\ $$$$\:−\mathrm{en}\:\mathrm{utilisant}\:\mathrm{la}\:\mathrm{definition}\:\mathrm{de}\:\mathrm{f} \\ $$$$−\mathrm{en}\:\mathrm{utilisant}\:\mathrm{la}\:\mathrm{matrice}\:{M}\: \\ $$$$\bullet\mathrm{3}\:\:\mathrm{determiner}\:\mathrm{bsse}\:\mathrm{de}\:\mathrm{Ker}\left(\:\boldsymbol{\mathrm{f}}\right)\:\mathrm{et}\:\mathrm{de}\:{I}\mathrm{m}\left(\boldsymbol{\mathrm{f}}\right)…
Question Number 204472 by mnjuly1970 last updated on 18/Feb/24 $$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Calculate}\:… \\ $$$$\:\:\:\:\:\:\:\Omega=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\lfloor\frac{\:\mathrm{1}}{\:\sqrt[{{k}}]{{e}}\:−\mathrm{1}}\:\rfloor\:=? \\ $$$$ \\ $$ Answered by TonyCWX08 last updated…
Question Number 204468 by MathedUp last updated on 18/Feb/24 $$\mathrm{How}\:\mathrm{Can}\:\mathrm{we}\:\mathrm{prove}\:\underset{{h}=−\infty} {\overset{\infty} {\sum}}\:{J}_{{h}} \left({z}\right)=\mathrm{1} \\ $$ Answered by Peace last updated on 19/Feb/24 $${J}_{{n}−\mathrm{1}} \left({x}\right)+{j}_{{n}+\mathrm{1}} \left({x}\right)=\frac{\mathrm{2}{n}}{{x}}{j}_{{n}}…
Question Number 204469 by DeArtist last updated on 18/Feb/24 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:=\:\begin{cases}{\mathrm{2},\:\mathrm{0}<\:{x}\:<\mathrm{2}}\\{−\mathrm{2},\:−\mathrm{2}\:<{x}\:<\:\mathrm{0}}\end{cases} \\ $$$$\mathrm{of}\:\mathrm{period}\:\mathrm{4} \\ $$$$\left(\mathrm{a}\right)\:\:\mathrm{sketch}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:{y}\:=\:{f}\left({x}\right)\:,\:\mathrm{for}\:−\mathrm{6}\:<\:{x}\:<\:\mathrm{6} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{Fourier}\:\mathrm{coefficient}\:{a}_{\mathrm{0}} ,\:{a}_{{n}} ,\:\mathrm{and}\:{b}_{{n}} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{write}\:\mathrm{down}\:\mathrm{the}\:\mathrm{Fourier}\:\mathrm{series}.\: \\ $$$$\left(\mathrm{d}\right)\:\mathrm{hence}\:\mathrm{show}\:\mathrm{that}\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}{n}−\mathrm{1}}\:=\:\frac{\pi}{\mathrm{4}}…
Question Number 204471 by Abdullahrussell last updated on 18/Feb/24 Answered by TonyCWX08 last updated on 18/Feb/24 $$ \\ $$ Answered by MM42 last updated on…
Question Number 204461 by MATHEMATICSAM last updated on 18/Feb/24 $$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$$\left({x}\:−\:\mathrm{12}\right)\left({x}\:−\:\mathrm{13}\right)\:=\:\frac{\mathrm{34}}{\mathrm{33}^{\mathrm{2}} } \\ $$ Answered by TonyCWX08 last updated on 18/Feb/24 $${x}^{\mathrm{2}} −\mathrm{25}{x}+\mathrm{156}\:=\:\frac{\mathrm{34}}{\mathrm{1089}} \\…
Question Number 204480 by EJJDJX last updated on 18/Feb/24 $${x}\:+\:\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{2}.\mathrm{05} \\ $$$${x}\:=\:? \\ $$ Commented by TonyCWX08 last updated on 19/Feb/24 $$ \\ $$$${x}^{\mathrm{2}} +\mathrm{1}=\:\mathrm{2}.\mathrm{05}{x}…
Question Number 204428 by sulaymonnorboyev140 last updated on 17/Feb/24 Commented by AST last updated on 17/Feb/24 $${Q}\mathrm{196938} \\ $$ Terms of Service Privacy Policy Contact:…