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Question Number 216487 Answers: 1 Comments: 2

Find the value of ω^7 + ω^8 + ω^(12) where ω is omega function.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\omega^{\mathrm{7}} \:\:+\:\:\omega^{\mathrm{8}} \:\:+\:\:\omega^{\mathrm{12}} \:\:\mathrm{where} \\ $$$$\omega\:\:\mathrm{is}\:\mathrm{omega}\:\mathrm{function}. \\ $$

Question Number 216486 Answers: 1 Comments: 0

∫_( 0) ^( 1) x(√(x ((x ((x ((x ...))^(1/5) ))^(1/4) ))^(1/3) )) dx

$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{x}\sqrt{\mathrm{x}\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:\sqrt[{\mathrm{4}}]{\mathrm{x}\:\:\sqrt[{\mathrm{5}}]{\mathrm{x}\:...}}}}\:\:\mathrm{dx} \\ $$

Question Number 216485 Answers: 2 Comments: 0

Solve for x in: i^x = 2

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:\:\mathrm{in}:\:\:\:\mathrm{i}^{\mathrm{x}} \:\:=\:\:\mathrm{2} \\ $$

Question Number 216478 Answers: 1 Comments: 1

Question Number 216477 Answers: 2 Comments: 0

Question Number 216471 Answers: 1 Comments: 3

Question Number 216445 Answers: 2 Comments: 2

Prove that Γ((1/2)) = (√π)

$$\mathrm{Prove}\:\mathrm{that}\:\:\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:\:=\:\:\sqrt{\pi} \\ $$

Question Number 216437 Answers: 3 Comments: 0

Question Number 216454 Answers: 0 Comments: 7

Reponse a l exercice N8: Reponses par ordre:(1,2,3,4,5,6) imsge 1 imsge 2 image 3 imsge 5 imsge 4 imsge 6

$$\mathrm{Reponse}\:\mathrm{a}\:\:\mathrm{l}\:\mathrm{exercice}\:\:\mathrm{N8}: \\ $$$$\mathrm{Reponses}\:\mathrm{par}\:\mathrm{ordre}:\left(\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\right) \\ $$$$\boldsymbol{\mathrm{imsge}}\:\mathrm{1}\: \\ $$$$\boldsymbol{\mathrm{imsge}}\:\mathrm{2} \\ $$$$\boldsymbol{\mathrm{image}}\:\mathrm{3} \\ $$$$\boldsymbol{\mathrm{imsge}}\:\mathrm{5} \\ $$$$\boldsymbol{\mathrm{imsge}}\:\mathrm{4} \\ $$$$\boldsymbol{\mathrm{imsge}}\:\mathrm{6} \\ $$

Question Number 216425 Answers: 2 Comments: 1

Question Number 216421 Answers: 1 Comments: 0

If asinθ + bcosθ = acosecθ + bsecθ then prove that each term is equal to (a^(2/3) − b^(2/3) )(√(a^(2/3) + b^(2/3) )).

$$\mathrm{If}\:{a}\mathrm{sin}\theta\:+\:{b}\mathrm{cos}\theta\:=\:{a}\mathrm{cosec}\theta\:+\:{b}\mathrm{sec}\theta\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{each}\:\mathrm{term}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left({a}^{\frac{\mathrm{2}}{\mathrm{3}}} \:−\:{b}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)\sqrt{{a}^{\frac{\mathrm{2}}{\mathrm{3}}} \:+\:{b}^{\frac{\mathrm{2}}{\mathrm{3}}} }. \\ $$

Question Number 216416 Answers: 1 Comments: 4

Question Number 216411 Answers: 1 Comments: 0

(dx/dx)

$$\frac{{dx}}{{dx}} \\ $$

Question Number 216408 Answers: 0 Comments: 1

∫_(−1) ^1 (1/x)(√((1+x)/(1−x)))ln(((2x^2 +2x+1)/(2x^2 −2x+1)))dx

$$\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\mathrm{1}}{{x}}\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\mathrm{ln}\left(\frac{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}\right){dx} \\ $$

Question Number 216390 Answers: 0 Comments: 3

f(x)=ax

$${f}\left({x}\right)={ax}\: \\ $$

Question Number 216381 Answers: 1 Comments: 0

∫(lnx)^2 dx

$$\int\left({lnx}\right)^{\mathrm{2}} {dx} \\ $$

Question Number 216388 Answers: 1 Comments: 1

Question Number 216387 Answers: 1 Comments: 0

Question Number 216372 Answers: 2 Comments: 0

∫((xe^x )/((x+1)^2 ))dx

$$\int\frac{{xe}^{{x}} }{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 216369 Answers: 2 Comments: 0

Question Number 216355 Answers: 1 Comments: 1

given that ϕ,β are the roots of the equation 3x2−x−5=0 from the equation whose roots are 2ϕ−1/β,2β−1/ϕ

$${given}\:{that}\:\varphi,\beta\:{are}\:{the}\:{roots}\:{of}\:{the}\:{equation}\:\mathrm{3}{x}\mathrm{2}−{x}−\mathrm{5}=\mathrm{0}\:{from}\:{the}\:{equation}\:{whose}\:{roots}\:{are}\:\mathrm{2}\varphi−\mathrm{1}/\beta,\mathrm{2}\beta−\mathrm{1}/\varphi \\ $$

Question Number 216352 Answers: 1 Comments: 1

Question Number 216351 Answers: 1 Comments: 0

Vector field F^→ ;R^3 →R^3 F^→ (x,y,z)=xye_1 ^→ −5ye_2 ^→ −3yze_3 ^→ ∫∫_(S;x^2 +y^2 +z^2 =r^2 ) F^→ ∙dS^→ = ?

$$\mathrm{Vector}\:\mathrm{field}\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}};\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}^{\mathrm{3}} \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)={xy}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −\mathrm{5}{y}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −\mathrm{3}{yz}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\underset{\mathcal{S};{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={r}^{\mathrm{2}} } {\int\int}\:\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathrm{S}}}=\:? \\ $$

Question Number 216350 Answers: 1 Comments: 0

S is the boundary surface of the surrounded by the cylinder x^2 +y^2 =9 and plane z=0 , z=2 and and vector Field F^→ ;R^3 →R^3 F^→ (x,y,z)=3ye_1 ^→ +yze_2 ^→ −xyz^5 e_3 ^→ ∫∫_(S) F^→ ∙dS^→ =?

$$\mathcal{S}\:\mathrm{is}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{surrounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{cylinder}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{9} \\ $$$$\mathrm{and}\:\mathrm{plane}\:{z}=\mathrm{0}\:,\:{z}=\mathrm{2}\:\mathrm{and} \\ $$$$\mathrm{and}\:\mathrm{vector}\:\mathrm{Field}\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}};\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}^{\mathrm{3}} \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)=\mathrm{3}{y}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} +{yz}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −{xyz}^{\mathrm{5}} \overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\underset{\mathcal{S}} {\int\int}\:\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathrm{S}}}=? \\ $$

Question Number 216332 Answers: 4 Comments: 0

Question Number 216324 Answers: 1 Comments: 1

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