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Author: Tinku Tara

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Question Number 67946 by Cmr 237 last updated on 02/Sep/19 $$\mathrm{use}\:\boldsymbol{\mathrm{Green}}−\boldsymbol{\mathrm{Riemann}}\:\boldsymbol{\mathrm{formuler}} \\ $$$$\mathrm{to}\:\mathrm{determined}: \\ $$$$\boldsymbol{\mathrm{I}}=\int\int_{\boldsymbol{\mathrm{D}}} \boldsymbol{\mathrm{xy}}\mathrm{dxdy} \\ $$$$\boldsymbol{\mathrm{D}}=\left\{\left(\mathrm{x},\mathrm{y}\right)\in\mathbb{R}^{\mathrm{2}} \mid\mathrm{x}\geqslant\mathrm{0};\mathrm{y}\geqslant;\mathrm{x}+{y}\leqslant\mathrm{1}\right\} \\ $$ Commented by mathmax by…

we-consider-that-application-n-1-det-M-n-R-R-A-det-A-1-verify-that-H-M-n-R-and-t-R-if-A-I-n-det-A-tH-1-t-Tr-H-t-2-suppose-that-A-GL-n-R-prouve-that-the-d

Question Number 133482 by AbderrahimMaths last updated on 22/Feb/21 $$\:\:\:\:{we}\:{consider}\:{that}\:{application}\:{n}\geqslant\mathrm{1} \\ $$$$\:\:{det}\::\:{M}_{{n}} \left(\mathbb{R}\right)\rightarrow\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{A} {det}\left({A}\right) \\ $$$$\mathrm{1}−{verify}\:{that}\:\forall{H}\in{M}_{{n}} \left(\mathbb{R}\right)\:{and}\:{t}\in\mathbb{R} \\ $$$$\:{if}\:{A}={I}_{{n}} \Rightarrow{det}\left({A}+{tH}\right)=\mathrm{1}+{t}.{Tr}\left({H}\right)+\circ\left({t}\right) \\ $$$$\mathrm{2}−{suppose}\:{that}:\:{A}\in{GL}_{{n}} \left(\mathbb{R}\right)…

e-y-2-2-dy-

Question Number 67942 by mhmd last updated on 02/Sep/19 $$\int{e}^{{y}^{\mathrm{2}} /\mathrm{2}} \:\:{dy} \\ $$ Commented by mr W last updated on 09/Feb/21 $$\int{e}^{\frac{{y}^{\mathrm{2}} }{\mathrm{2}}} {dy}=\sqrt{\frac{\pi}{\mathrm{2}}}\:{erfi}\left(\frac{{y}}{\:\sqrt{\mathrm{2}}}\right)+{C}…

Question-67939

Question Number 67939 by ramirez105 last updated on 02/Sep/19 Commented by mr W last updated on 02/Sep/19 $${sir},\:{you}\:{got}\:{y}^{\mathrm{2}} \left({y}+\mathrm{2}{x}\right)={C},\:{but}\:{this} \\ $$$${doesn}'{t}\:{satisfy}\:{the}\:{original}\:{equ}. \\ $$$${is}\: \\ $$$$\frac{{dy}}{{y}}\:=−\frac{{dx}}{\mathrm{2}{x}+\mathrm{3}{y}}\:\Rightarrow\int\:\frac{{dy}}{{y}}\:=−\int\frac{{dx}}{\mathrm{2}{x}+\mathrm{3}{y}}\:+{c}…

Question-67937

Question Number 67937 by A8;15: last updated on 02/Sep/19 Commented by mathmax by abdo last updated on 02/Sep/19 $${at}\:{form}\:{of}\:{serie} \\ $$$${I}\:=\int\sqrt{{e}^{{x}} }{dx}\:=\:\int\:\:{e}^{\frac{{x}}{\mathrm{2}}} {dx}\:=\int\left(\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(\frac{{x}}{\mathrm{2}}\right)^{{n}}…

According-to-Wikipedia-and-WolframAlpha-the-sign-function-sgn-x-is-defined-as-sgn-x-x-x-x-x-for-x-0-and-satisfies-sgn-x-x-1-x-but-sgn-0-0-In-short-sgn-x-1-f

Question Number 2400 by Filup last updated on 19/Nov/15 $$\mathrm{According}\:\mathrm{to}\:\mathrm{Wikipedia}\:\mathrm{and}\:\mathrm{WolframAlpha}, \\ $$$$\mathrm{the}\:\mathrm{sign}\:\mathrm{function},\:\mathrm{sgn}\left({x}\right),\:\mathrm{is}\:\mathrm{defined}\:\mathrm{as}: \\ $$$$ \\ $$$$\mathrm{sgn}\left({x}\right)\equiv\frac{{x}}{\mid{x}\mid}=\frac{\mid{x}\mid}{{x}}\:\:\:\mathrm{for}\:{x}\neq\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{satisfies}: \\ $$$$\mathrm{sgn}\left({x}\right)=\sqrt{{x}}\sqrt{\frac{\mathrm{1}}{{x}}} \\ $$$$\boldsymbol{{but}} \\ $$$$\mathrm{sgn}\left(\mathrm{0}\right)=\mathrm{0} \\…