Question Number 220198 by SdC355 last updated on 07/May/25 Commented by SdC355 last updated on 08/May/25 $$\mathrm{i}\:\mathrm{already}\:\mathrm{know}\:\mathrm{and}\:\mathrm{understand}\:\mathrm{about}\:\:\mathrm{operator}\:\overset{\rightarrow} {\bigtriangledown}×\overset{\rightarrow} {\boldsymbol{\mathrm{F}}} \\ $$$$\overset{\rightarrow} {\bigtriangledown}×\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}=\begin{vmatrix}{\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} }&{\overset{\rightarrow}…
Question Number 220121 by SdC355 last updated on 06/May/25 $$\mathrm{Let}\:{H}_{{h}} ={p}_{{h}+\mathrm{1}} /{p}_{{h}} \:,\:{p}_{{h}} \in\mathbb{P}\:,\:{p}_{\mathrm{1}} =\mathrm{2} \\ $$$$\underset{{h}=\mathrm{1}} {\overset{\infty} {\prod}}\:{H}_{{h}} =??\:\left(\underset{{h}=\mathrm{1}} {\overset{\infty} {\prod}}\:{H}_{{h}} =\frac{\mathrm{3}}{\mathrm{2}}\centerdot\frac{\mathrm{5}}{\mathrm{3}}\centerdot\frac{\mathrm{7}}{\mathrm{5}}………\right) \\ $$…
Question Number 220116 by SdC355 last updated on 06/May/25 $$\mathrm{evaluate} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{{J}_{\nu} \left({z}\right){e}^{−{zt}} }{{z}^{\mathrm{2}} +\alpha^{\mathrm{2}} }\:\mathrm{d}{z}\:,\:\alpha\in\mathbb{R}\backslash\left\{\mathrm{0}\right\} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{{J}_{\nu} \left({z}\right){e}^{−{zt}} }{\left({z}+\boldsymbol{{i}}\alpha\right)\left({z}−\boldsymbol{{i}}\alpha\right)}\:\mathrm{d}{z}= \\…
Question Number 220141 by MrGaster last updated on 06/May/25 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{{m}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({n}^{\mathrm{2}} +{m}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }=? \\ $$ Answered by Nicholas666 last updated on…
Question Number 220081 by SdC355 last updated on 05/May/25 Commented by MathematicalUser2357 last updated on 05/May/25 $$\boldsymbol{{Elementary}}\:\boldsymbol{{math}}\:\boldsymbol{{problem}}\:\boldsymbol{{that}}\:\mathrm{50\%}\:\boldsymbol{{of}}\:\boldsymbol{{adults}}\:\boldsymbol{{failed}} \\ $$$${Find}\:{the}\:{angle}\:{to}\:{put}\:{in}\:'?'. \\ $$ Commented by MathematicalUser2357 last…
Question Number 219952 by Mamadi last updated on 04/May/25 $${solve}\:{the}\:{system}\:{differential} \\ $$$${x}'=\mathrm{3}{x}−{y}+{z} \\ $$$${y}'=\mathrm{2}{x}+{z} \\ $$$${z}'=−\mathrm{2}{x}+{y} \\ $$$${with}\:{x},{y},{and}\:{z}\:{are}\:{the}\:{function}\:{of}\: \\ $$$${t}. \\ $$$$ \\ $$ Commented…
Question Number 220015 by SdC355 last updated on 04/May/25 $$\int_{\mathrm{0}} ^{\:\infty} \:\mid\mid{J}_{\nu} \left({r}\right)\mid\mid{e}^{−{rt}} \:\mathrm{d}{r}=\underset{{h}=\mathrm{1}} {\overset{\infty} {\sum}}\:\int_{{z}_{{h}} } ^{\:{z}_{{h}+\mathrm{1}} } \:{J}_{\nu} \left({r}\right){e}^{−{rt}} \mathrm{d}{r} \\ $$$${z}_{{j}} \:\mathrm{is}\:\mathrm{point}\:\mathrm{of}\:\:{J}_{\nu}…
Question Number 220066 by SdC355 last updated on 04/May/25 $$\mathrm{evaluate} \\ $$$$−\frac{\mathrm{csc}\left(\pi{s}\right)}{\boldsymbol{{i}}\pi}\int_{\:\boldsymbol{\mathcal{C}}} \:\left(−{t}\right)^{{s}−\mathrm{1}} {e}^{−{t}} \:\mathrm{d}{t}\:,\:\mathrm{path}\:\boldsymbol{\mathcal{C}};\left(−\infty,\infty\right) \\ $$$$−\frac{\boldsymbol{\Gamma}\left(\mathrm{1}−{s}\right)}{\mathrm{2}\pi\boldsymbol{{i}}}\:\int_{\:\boldsymbol{\mathcal{C}}} \:\frac{\left(−{t}\right)^{{s}−\mathrm{1}} }{{e}^{{t}} −\mathrm{1}}\:\mathrm{d}{t}\:,\:\mathrm{path}\:\boldsymbol{\mathcal{C}};\left(−\infty,\infty\right) \\ $$ Terms of Service…
Question Number 219996 by SdC355 last updated on 04/May/25 $$\mathrm{Solve}\:\mathrm{Equation} \\ $$$$\frac{\mathrm{d}{x}\left({t}\right)}{\mathrm{d}{t}}=\mathrm{2}{x}\left({t}\right)+{y}\left({t}\right) \\ $$$$\frac{\mathrm{d}{y}\left({t}\right)}{\mathrm{d}{t}}=−\mathrm{3}{y}\left({t}\right) \\ $$$$\begin{pmatrix}{{x}^{\left(\mathrm{1}\right)} \left({t}\right)}\\{{y}^{\left(\mathrm{1}\right)} \left({t}\right)}\end{pmatrix}=\begin{pmatrix}{\mathrm{2}}&{\:\:\:\:\mathrm{1}}\\{\mathrm{0}}&{−\mathrm{3}}\end{pmatrix}\begin{pmatrix}{{x}\left({t}\right)}\\{{y}\left({t}\right)}\end{pmatrix} \\ $$$$\mathrm{A}=\begin{pmatrix}{\mathrm{2}}&{\:\:\:\:\mathrm{1}}\\{\mathrm{0}}&{−\mathrm{3}}\end{pmatrix} \\ $$$$\mathrm{det}\left\{\mathrm{A}−\boldsymbol{\lambda}\mathrm{E}\right\}=\mathrm{0} \\ $$$$\mathrm{det}\left\{\begin{pmatrix}{\mathrm{2}}&{\:\:\:\:\mathrm{1}}\\{\mathrm{0}}&{−\mathrm{3}}\end{pmatrix}−\begin{pmatrix}{\boldsymbol{\lambda}}&{\mathrm{0}}\\{\mathrm{0}}&{\boldsymbol{\lambda}}\end{pmatrix}\right\}=\mathrm{0} \\…
Question Number 219890 by SdC355 last updated on 03/May/25 $$\mathrm{Find}\:\mathrm{Maxima}\: \\ $$$${x}+{y}\:\mathrm{where}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={r}^{\mathrm{2}} \:\left(\mathrm{use}\:\mathrm{Lagrange}\:\mathrm{Method}\right) \\ $$ Answered by MrGaster last updated on 03/May/25 $$\bigtriangledown\left({x}+{y}\right)=\lambda\bigtriangledown\left({x}^{\mathrm{2}}…