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Question Number 30000 Answers: 1 Comments: 1

If cos α = sin β sin φ=sin γ cos ψ cos β = sin γ sin ψ =sin α cos θ cos γ = sin α sin θ =sin β cos φ then find cos α, cos β , cos γ briefly and if possible linearly in terms of only sin θ, cos θ, sin φ, cos φ, sin ψ, cos ψ .

$${If}\:\mathrm{cos}\:\alpha\:=\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\phi=\mathrm{sin}\:\gamma\:\mathrm{cos}\:\psi \\ $$$$\:\:\:\:\:\:\mathrm{cos}\:\beta\:=\:\mathrm{sin}\:\gamma\:\mathrm{sin}\:\psi\:=\mathrm{sin}\:\alpha\:\mathrm{cos}\:\theta \\ $$$$\:\:\:\:\:\:\mathrm{cos}\:\gamma\:=\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\theta\:=\mathrm{sin}\:\beta\:\mathrm{cos}\:\phi \\ $$$${then}\:{find}\:\:\mathrm{cos}\:\alpha,\:\mathrm{cos}\:\beta\:,\:\mathrm{cos}\:\gamma\:\:\: \\ $$$${briefly}\:{and}\:{if}\:{possible}\:{linearly} \\ $$$${in}\:{terms}\:{of}\:{only}\:\mathrm{sin}\:\theta,\:\mathrm{cos}\:\theta, \\ $$$$\mathrm{sin}\:\phi,\:\mathrm{cos}\:\phi,\:\mathrm{sin}\:\psi,\:\mathrm{cos}\:\psi\:. \\ $$

Question Number 29960 Answers: 1 Comments: 0

Question Number 29957 Answers: 1 Comments: 0

∫3xdx

$$\int\mathrm{3}{x}\mathrm{d}{x} \\ $$

Question Number 30032 Answers: 0 Comments: 3

(x+1)^x −x^((x+1)) =1 x=?

$$\left({x}+\mathrm{1}\right)^{{x}} −{x}^{\left({x}+\mathrm{1}\right)} =\mathrm{1} \\ $$$${x}=? \\ $$

Question Number 29953 Answers: 0 Comments: 2

Question Number 29924 Answers: 1 Comments: 5

Question Number 29909 Answers: 2 Comments: 1

please solve this: (√(30+12(√6)))

$${please}\:{solve}\:{this}:\:\:\sqrt{\mathrm{30}+\mathrm{12}\sqrt{\mathrm{6}}} \\ $$

Question Number 29907 Answers: 1 Comments: 5

Question Number 29896 Answers: 5 Comments: 1

Question Number 30655 Answers: 0 Comments: 0

Question Number 29880 Answers: 0 Comments: 3

Question Number 29875 Answers: 0 Comments: 0

Prove the convergence or divergent of (((n − 1)/n))_(n = 1) ^∞

$$\mathrm{Prove}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{or}\:\mathrm{divergent}\:\mathrm{of}\:\:\:\:\:\:\:\:\:\:\left(\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}}\right)_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \\ $$$$ \\ $$

Question Number 29877 Answers: 0 Comments: 2

Question Number 29857 Answers: 0 Comments: 0

find ∫_0 ^(+∞) ((ln(x))/((1+x)^3 ))dx .

$${find}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{ln}\left({x}\right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{3}} }{dx}\:. \\ $$

Question Number 29856 Answers: 0 Comments: 1

find ∫_0 ^(2π) ((cos(nθ))/(2+3cosθ))dθ . n from N.

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}\left({n}\theta\right)}{\mathrm{2}+\mathrm{3}{cos}\theta}{d}\theta\:.\:\:{n}\:{from}\:{N}. \\ $$

Question Number 29855 Answers: 1 Comments: 1

find ∫_0 ^∞ (x^2 /((1+x^2 )( 3+x^2 )))dx .

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\:\mathrm{3}+{x}^{\mathrm{2}} \right)}{dx}\:. \\ $$

Question Number 29854 Answers: 0 Comments: 1

find ∫_(−∞) ^(+∞) (((x^2 +2)dx)/(x^4 +8x^2 −16x +20)) .

$${find}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\:\:\frac{\left({x}^{\mathrm{2}} +\mathrm{2}\right){dx}}{{x}^{\mathrm{4}} \:+\mathrm{8}{x}^{\mathrm{2}} −\mathrm{16}{x}\:+\mathrm{20}}\:. \\ $$

Question Number 29853 Answers: 0 Comments: 1

find ∫_(−∞) ^(+∞) (dx/(x^2 +2ix +2−4i)) .

$${find}\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{ix}\:+\mathrm{2}−\mathrm{4}{i}}\:. \\ $$

Question Number 29852 Answers: 0 Comments: 0

let f(z) =z cos^2 ((π/z)) find Res(f,0).

$${let}\:{f}\left({z}\right)\:={z}\:{cos}^{\mathrm{2}} \left(\frac{\pi}{{z}}\right)\:\:{find}\:{Res}\left({f},\mathrm{0}\right). \\ $$

Question Number 29851 Answers: 0 Comments: 0

let give f(z)=((tanz −z)/((1−cosz)^2 )) find Res(f,0).

$${let}\:{give}\:{f}\left({z}\right)=\frac{{tanz}\:−{z}}{\left(\mathrm{1}−{cosz}\right)^{\mathrm{2}} }\:\:{find}\:{Res}\left({f},\mathrm{0}\right). \\ $$

Question Number 29850 Answers: 0 Comments: 0

find I = ∫_0 ^∞ (((1+x)^(−(1/4)) −(1+x)^(−(3/4)) )/x)dx .

$${find}\:\:{I}\:\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} \:\:−\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} }{{x}}{dx}\:. \\ $$

Question Number 29849 Answers: 0 Comments: 1

let give a>0 ,b>0 find the vslue of ∫_0 ^(+∞) ((e^(−at) −e^(−bt) )/t) cos(xt)dt .

$${let}\:{give}\:{a}>\mathrm{0}\:,{b}>\mathrm{0}\:{find}\:{the}\:{vslue}\:{of}\: \\ $$$$\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{e}^{−{at}} \:−{e}^{−{bt}} }{{t}}\:{cos}\left({xt}\right){dt}\:. \\ $$

Question Number 29848 Answers: 0 Comments: 1

find Σ_(k=0) ^n cos(kx) and Σ_(k=0) ^n sin(kx) .

$${find}\:\:\sum_{{k}=\mathrm{0}} ^{{n}} {cos}\left({kx}\right)\:{and}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{sin}\left({kx}\right)\:. \\ $$

Question Number 29847 Answers: 0 Comments: 0

θ ∈]0,π[ find he values of Σ_(n=1) ^∞ (1/n)cos(nθ) and Σ_(n=1) ^∞ (1/n)sin(nθ) .

$$\left.\theta\:\in\right]\mathrm{0},\pi\left[\:\:\:{find}\:{he}\:{values}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}}{cos}\left({n}\theta\right)\:{and}\right. \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}}{sin}\left({n}\theta\right)\:. \\ $$

Question Number 29846 Answers: 0 Comments: 1

give the developpement at integr series for f(x)=((ln(1+x)−ln(1−x))/x) 2)find lim_(x→0) f(x).

$${give}\:{the}\:{developpement}\:\:{at}\:{integr}\:{series}\:{for} \\ $$$${f}\left({x}\right)=\frac{{ln}\left(\mathrm{1}+{x}\right)−{ln}\left(\mathrm{1}−{x}\right)}{{x}} \\ $$$$\left.\mathrm{2}\right){find}\:\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:{f}\left({x}\right). \\ $$

Question Number 29845 Answers: 0 Comments: 2

find lim_(x→0) ((tanx −x−(1/3)x^3 )/x^5 ) .

$${find}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\:\:\frac{{tanx}\:−{x}−\frac{\mathrm{1}}{\mathrm{3}}{x}^{\mathrm{3}} }{{x}^{\mathrm{5}} }\:\:. \\ $$

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