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Question Number 146977    Answers: 2   Comments: 0

find (1) ∫_C (e^z^2 /(z^2 +4z+3))dz ,C:∣z−2∣=5 (2)∫_(−∞) ^( ∞) ((cosx)/(x^2 +2x+2))dx

$${find} \\ $$$$\left(\mathrm{1}\right)\:\int_{{C}} \:\frac{{e}^{{z}^{\mathrm{2}} } }{{z}^{\mathrm{2}} +\mathrm{4}{z}+\mathrm{3}}{dz}\:\:,{C}:\mid{z}−\mathrm{2}\mid=\mathrm{5} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\int_{−\infty} ^{\:\infty} \frac{{cosx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}}{dx} \\ $$

Question Number 146975    Answers: 1   Comments: 0

find laurant series f(z)=((z^2 −2z+3)/(z−2)) ,∣z−1∣>1

$${find}\:{laurant}\:{series}\:{f}\left({z}\right)=\frac{{z}^{\mathrm{2}} −\mathrm{2}{z}+\mathrm{3}}{{z}−\mathrm{2}}\:,\mid{z}−\mathrm{1}\mid>\mathrm{1} \\ $$

Question Number 146964    Answers: 1   Comments: 0

Simplify: (((√2) ∙ (√(2 + (√2))) ∙ (√(2 - (√2))))/( (√(2(√2))))) = ?

$${Simplify}: \\ $$$$\frac{\sqrt{\mathrm{2}}\:\centerdot\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}}}\:\centerdot\:\sqrt{\mathrm{2}\:-\:\sqrt{\mathrm{2}}}}{\:\sqrt{\mathrm{2}\sqrt{\mathrm{2}}}}\:=\:? \\ $$

Question Number 146962    Answers: 1   Comments: 0

Question Number 146961    Answers: 1   Comments: 0

(√(sin(x))) ∙ cos(x) < 0

$$\sqrt{{sin}\left({x}\right)}\:\centerdot\:{cos}\left({x}\right)\:<\:\mathrm{0} \\ $$

Question Number 146960    Answers: 2   Comments: 0

Question Number 146959    Answers: 1   Comments: 0

∫ln(1+(√(x^2 +2x+4)))dx

$$\int{ln}\left(\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}}\right){dx} \\ $$

Question Number 147764    Answers: 1   Comments: 0

Question Number 146943    Answers: 3   Comments: 0

b_(n+2) ∙ b_(n+3) ∙ b_(n+4) = 3^(3n+3) geometric series b_8 = ?

$${b}_{\boldsymbol{{n}}+\mathrm{2}} \:\centerdot\:{b}_{\boldsymbol{{n}}+\mathrm{3}} \:\centerdot\:{b}_{\boldsymbol{{n}}+\mathrm{4}} \:=\:\mathrm{3}^{\mathrm{3}\boldsymbol{{n}}+\mathrm{3}} \\ $$$${geometric}\:{series}\:\:\boldsymbol{{b}}_{\mathrm{8}} \:=\:? \\ $$

Question Number 146938    Answers: 0   Comments: 0

Question Number 146936    Answers: 3   Comments: 0

{ ((x^2 +2y^2 +xy=37)),((y^2 +2x^2 +2xy=26)) :} ⇒ x^2 +y^2 =?

$$\begin{cases}{{x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} +{xy}=\mathrm{37}}\\{{y}^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{xy}=\mathrm{26}}\end{cases}\:\Rightarrow\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =? \\ $$

Question Number 146933    Answers: 0   Comments: 0

.....# advanced calculu#...... I := ∫_(−∞) ^( +∞) sin(cosh(x).cos(sinhx))dx=? ....solution .... I:=(1/2) ∫_(−∞) ^( +∞) {sin (cosh(x)+sinh(x))+sin(cosh(x)−sinh (x))} :=_(sinh(x)=((e^( x) −e^( −x) )/2)) ^(cosh(x)=((e^( x) +e^( −x) )/2)) (1/2) ∫_(−∞) ^( +∞) {sin(e^x )+sin (e^( −x) )}dx := (1/2) ∫_(−∞) ^( ∞) sin(e^( x) )dx +[(1/2)∫_(−∞) ^( +∞) sin(e^( x) )dx :: x=^(sub) −x] := ∫_(−∞) ^( +∞) sin(e^( x) ) dx =^(e^( x) =y) ∫_0 ^( ∞) ((sin(t))/t) dt ...... I:= (π/2) ..... ...m.n.1970...

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....#\:{advanced}\:\:{calculu}#...... \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\:\int_{−\infty} ^{\:+\infty} {sin}\left({cosh}\left({x}\right).{cos}\left({sinhx}\right)\right){dx}=? \\ $$$$\:\:\:\:\:....{solution}\:.... \\ $$$$\:\:\:\:\:\:\:\mathrm{I}:=\frac{\mathrm{1}}{\mathrm{2}}\:\int_{−\infty} ^{\:+\infty} \left\{{sin}\:\left({cosh}\left({x}\right)+{sinh}\left({x}\right)\right)+{sin}\left({cosh}\left({x}\right)−{sinh}\:\left({x}\right)\right)\right\} \\ $$$$\:\:\:\:\:\:\:\:\::\underset{{sinh}\left({x}\right)=\frac{{e}^{\:{x}} −{e}^{\:−{x}} }{\mathrm{2}}} {\overset{{cosh}\left({x}\right)=\frac{{e}^{\:{x}} +{e}^{\:−{x}} }{\mathrm{2}}} {=}}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\int_{−\infty} ^{\:+\infty} \left\{{sin}\left({e}^{{x}} \right)+{sin}\:\left({e}^{\:−{x}} \right)\right\}{dx} \\ $$$$\:\:\:\:\:\:\:\:\::=\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\int_{−\infty} ^{\:\infty} {sin}\left({e}^{\:{x}} \right){dx}\:+\left[\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{\:+\infty} {sin}\left({e}^{\:{x}} \right){dx}\:::\:\:{x}\overset{{sub}} {=}−{x}\right] \\ $$$$\:\:\:\:\:\:\:\::=\:\int_{−\infty} ^{\:+\infty} {sin}\left({e}^{\:{x}} \:\right)\:{dx}\:\overset{{e}^{\:{x}} ={y}} {=}\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({t}\right)}{{t}}\:{dt}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:......\:\mathrm{I}:=\:\frac{\pi}{\mathrm{2}}\:..... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...{m}.{n}.\mathrm{1970}... \\ $$$$\: \\ $$$$ \\ $$

Question Number 146929    Answers: 1   Comments: 5

Question Number 146927    Answers: 1   Comments: 0

Question Number 146926    Answers: 1   Comments: 0

Question Number 146924    Answers: 1   Comments: 0

Montrer que Σ_(k=0) ^(2n−1) cos^(2n) (𝛉+((k𝛑)/(2n)))= ((nC_(2n) ^n )/2^(2n−1) )

$$\boldsymbol{\mathrm{Montrer}}\:\boldsymbol{\mathrm{que}} \\ $$$$\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}} {\sum}}\boldsymbol{{cos}}^{\mathrm{2}\boldsymbol{{n}}} \left(\boldsymbol{\theta}+\frac{\boldsymbol{{k}\pi}}{\mathrm{2}\boldsymbol{{n}}}\right)=\:\frac{\boldsymbol{{nC}}_{\mathrm{2}\boldsymbol{{n}}} ^{\boldsymbol{{n}}} }{\mathrm{2}^{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}} } \\ $$

Question Number 146923    Answers: 1   Comments: 0

if arg (((i - z)/i)) = (π/4) find RemZ + ImZ = ?

$${if}\:\:\:\:{arg}\:\left(\frac{{i}\:-\:{z}}{{i}}\right)\:=\:\frac{\pi}{\mathrm{4}} \\ $$$${find}\:\:\:\:{RemZ}\:+\:{ImZ}\:=\:? \\ $$

Question Number 146914    Answers: 2   Comments: 0

∣x^2 −3x−4∣ = ∣x−4∣ ⇒ x=?

$$\mid{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}\mid\:=\:\mid{x}−\mathrm{4}\mid\:\Rightarrow\:{x}=? \\ $$

Question Number 146913    Answers: 1   Comments: 0

ax=by=cz=(2/3) and ab+bc+ac=36abc find x+y+z=?

$${ax}={by}={cz}=\frac{\mathrm{2}}{\mathrm{3}}\:{and}\:{ab}+{bc}+{ac}=\mathrm{36}{abc} \\ $$$${find}\:\:{x}+{y}+{z}=? \\ $$

Question Number 146906    Answers: 0   Comments: 0

Question Number 147078    Answers: 0   Comments: 1

Question Number 146904    Answers: 0   Comments: 0

F = ((Gm_1 m_2 )/r^2 ) Find the value of r with the following equation.

$$\boldsymbol{\mathrm{F}}\:=\:\frac{\boldsymbol{\mathrm{Gm}}_{\mathrm{1}} \boldsymbol{\mathrm{m}}_{\mathrm{2}} }{\boldsymbol{\mathrm{r}}^{\mathrm{2}} } \\ $$$$\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{r}}\:\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\: \\ $$$$\boldsymbol{\mathrm{equation}}. \\ $$

Question Number 146902    Answers: 1   Comments: 0

let α and β roots of z^2 +3z+5=0 simlify U_n = Σ_(k=0) ^n (α^k +β^k ) and V_n =Σ_(k=0) ^n ((1/α^k )+(1/β^k ))

$$\mathrm{let}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{roots}\:\mathrm{of}\:\:\mathrm{z}^{\mathrm{2}} +\mathrm{3z}+\mathrm{5}=\mathrm{0} \\ $$$$\mathrm{simlify}\:\mathrm{U}_{\mathrm{n}} =\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\left(\alpha^{\mathrm{k}} \:+\beta^{\mathrm{k}} \right) \\ $$$$\mathrm{and}\:\mathrm{V}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\left(\frac{\mathrm{1}}{\alpha^{\mathrm{k}} }+\frac{\mathrm{1}}{\beta^{\mathrm{k}} }\right) \\ $$

Question Number 146901    Answers: 1   Comments: 0

g(x)=cos(2arcsinx) calculate (dg/dx) and (d^2 g/dx^2 ) 2)find ∫_(−(1/2)) ^(1/2) g(x)dx

$$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{cos}\left(\mathrm{2arcsinx}\right)\:\: \\ $$$$\mathrm{calculate}\:\frac{\mathrm{dg}}{\mathrm{dx}}\:\mathrm{and}\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{g}}{\mathrm{dx}^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\mathrm{find}\:\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\mathrm{g}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 146899    Answers: 1   Comments: 0

f(x)=sin^5 x calculate f^((5)) ((π/2))

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sin}^{\mathrm{5}} \mathrm{x}\:\:\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{5}\right)} \left(\frac{\pi}{\mathrm{2}}\right) \\ $$

Question Number 146898    Answers: 2   Comments: 0

calculate ∫_0 ^∞ ((cosx)/((x^2 +1)(x^2 +2)(x^2 +3)))dx

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

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