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Question Number 189325    Answers: 2   Comments: 0

prove Ω= ∫_0 ^(π/2) (( cos(x)+cos(5x))/(1+ 2sin(x))) =^( ?) (3/2)

$$ \\ $$$$\:\:\:\:\:{prove} \\ $$$$ \\ $$$$\:\:\Omega=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\:{cos}\left({x}\right)+{cos}\left(\mathrm{5}{x}\right)}{\mathrm{1}+\:\mathrm{2}{sin}\left({x}\right)}\:\overset{\:?} {=}\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$ \\ $$

Question Number 189323    Answers: 1   Comments: 0

Question Number 189319    Answers: 0   Comments: 4

Question Number 189309    Answers: 1   Comments: 0

Question Number 189304    Answers: 2   Comments: 1

Question Number 189302    Answers: 1   Comments: 2

Q: find the number of the solutions for : ( x_( 1) + x_( 2) )^( 3) + x_( 3) + x_( 4) + x_( 5) =11 Hint: ( x_( i) ∈ Z^( +) ∪ { 0 } )

$$ \\ $$$$\:\:\:\:{Q}:\:\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{the}\:\:\mathrm{solutions}\:\:\mathrm{for}\:: \\ $$$$ \\ $$$$\:\:\left(\:{x}_{\:\mathrm{1}} \:+\:{x}_{\:\mathrm{2}} \:\right)^{\:\mathrm{3}} \:+\:{x}_{\:\mathrm{3}} \:+\:{x}_{\:\mathrm{4}} \:+\:{x}_{\:\mathrm{5}} \:=\mathrm{11} \\ $$$$\:\:\: \\ $$$$\:\:\:\:{Hint}:\:\:\:\left(\:{x}_{\:{i}} \:\:\in\:\:\mathbb{Z}^{\:\:+} \:\:\cup\:\left\{\:\mathrm{0}\:\right\}\:\:\right) \\ $$$$\: \\ $$

Question Number 189293    Answers: 1   Comments: 0

Question Number 189292    Answers: 0   Comments: 2

Question Number 189291    Answers: 0   Comments: 0

Question Number 189290    Answers: 1   Comments: 0

Question Number 189285    Answers: 2   Comments: 0

f(x) is continous function on R and lim_(x→1) ((f(((x+1)/x))−6)/((((x−1)/x))^2 ))=2 Evalute : lim_(x→1) (((√(f(x)+x))−x)/((x−1)))=¿

$${f}\left({x}\right)\:{is}\:{continous}\:{function}\:{on}\:{R} \\ $$$${and}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{f}\left(\frac{{x}+\mathrm{1}}{{x}}\right)−\mathrm{6}}{\left(\frac{{x}−\mathrm{1}}{{x}}\right)^{\mathrm{2}} }=\mathrm{2} \\ $$$${Evalute}\::\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\sqrt{{f}\left({x}\right)+{x}}−{x}}{\left({x}−\mathrm{1}\right)}=¿ \\ $$

Question Number 189270    Answers: 2   Comments: 1

Question Number 189269    Answers: 1   Comments: 0

Question Number 189267    Answers: 3   Comments: 1

Question Number 189266    Answers: 1   Comments: 0

∫_0 ^(π/2) (((tan x))^(1/3) /(1+sin 2x)) dx =?

$$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{tan}\:\mathrm{x}}}{\mathrm{1}+\mathrm{sin}\:\mathrm{2x}}\:\mathrm{dx}\:=? \\ $$

Question Number 189263    Answers: 0   Comments: 1

evaluate ∫∫_E ∫15Zdv, where E is the region between 2x+y+z=4 and 4x+4y+2z=20 which is in front of the region in the yz plane bounded by z=2y^2 and z=(√(4y))

$$\boldsymbol{{evaluate}}\:\int\int_{\boldsymbol{\mathrm{E}}} \int\mathrm{15}{Zdv},\:{where}\:{E} \\ $$$$\:{is}\:{the}\:{region}\:{between}\:\mathrm{2}{x}+{y}+{z}=\mathrm{4} \\ $$$$\:{and}\:\mathrm{4}{x}+\mathrm{4}{y}+\mathrm{2}{z}=\mathrm{20}\:{which}\:{is}\:{in}\: \\ $$$${front}\:{of}\:{the}\:{region}\:{in}\:{the}\:{yz}\:{plane}\: \\ $$$${bounded}\:{by}\:{z}=\mathrm{2}{y}^{\mathrm{2}} \:{and}\:{z}=\sqrt{\mathrm{4}{y}} \\ $$

Question Number 189257    Answers: 1   Comments: 0

determine the surface area of the portion of z=13−4x^2 −4y^2 that is above z=1 with x≤0 and y≥0

$$\boldsymbol{\mathrm{determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{surface}}\:\boldsymbol{\mathrm{area}}\: \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{portion}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{z}}=\mathrm{13}−\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{y}}^{\mathrm{2}} \: \\ $$$$\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{above}}\:\boldsymbol{\mathrm{z}}=\mathrm{1}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{x}}\leq\mathrm{0}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}}\geq\mathrm{0} \\ $$

Question Number 189256    Answers: 1   Comments: 0

Prove that sin10° = (1/2)(√(2−(√(2+(√(2+(√(2−(√(2+(√(2+(√(2−(√(2+(√(2+(√(2−(√(2+(√(2+(√(2−...........∞))))))))))))))))))))))))))

$${Prove}\:{that} \\ $$$$\mathrm{sin10}°\:=\:\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{2}−\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}−\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}−\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}−\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}−...........\infty}}}}}}}}}}}}} \\ $$

Question Number 189254    Answers: 1   Comments: 0

Question Number 189250    Answers: 0   Comments: 1

Question Number 189248    Answers: 2   Comments: 0

Question Number 189242    Answers: 0   Comments: 0

Question Number 189233    Answers: 1   Comments: 2

1•Evaluer :Aire(A′B′C′D′) 2•En deduire:((Aire(A′B′C′D′))/(Aire(ABCD)))

$$\mathrm{1}\bullet{Evaluer}\::\boldsymbol{{Aire}}\left(\boldsymbol{{A}}'\boldsymbol{{B}}'\boldsymbol{{C}}'\boldsymbol{{D}}'\right) \\ $$$$\mathrm{2}\bullet{En}\:{deduire}:\frac{\boldsymbol{{Aire}}\left(\boldsymbol{{A}}'\boldsymbol{{B}}'\boldsymbol{{C}}'\boldsymbol{{D}}'\right)}{\boldsymbol{{Aire}}\left(\boldsymbol{{ABCD}}\right)} \\ $$

Question Number 189223    Answers: 0   Comments: 2

who did discoer the light′s speed and by which method?

$${who}\:{did}\:{discoer}\:{the}\:{light}'{s}\:{speed}\:{and} \\ $$$${by}\:{which}\:{method}? \\ $$

Question Number 189212    Answers: 0   Comments: 0

Question Number 189208    Answers: 2   Comments: 0

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