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Relation and FunctionsQuestion and Answers: Page 6

Question Number 152671 Answers: 3 Comments: 2

Question Number 152151 Answers: 3 Comments: 0

Question Number 151897 Answers: 1 Comments: 0

Question Number 151863 Answers: 2 Comments: 0

lim_(x−0) ((1−Π_(k=1) ^n cos(kx))/x^2 )=????

$$\: \\ $$$$\boldsymbol{{li}}\underset{\boldsymbol{{x}}−\mathrm{0}} {\boldsymbol{{m}}}\frac{\mathrm{1}−\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\prod}}\boldsymbol{{cos}}\left(\boldsymbol{{kx}}\right)}{\boldsymbol{{x}}^{\mathrm{2}} }=???? \\ $$$$ \\ $$

Question Number 151859 Answers: 0 Comments: 2

Question Number 151742 Answers: 1 Comments: 0

F (x ):= ((log (sin(x) +cos (x)))/(log (sin(2x)))) find the Domain of F ... D_( F) =?

$$\:\: \\ $$$$\:\:\:\mathrm{F}\:\left({x}\:\right):=\:\frac{{log}\:\left({sin}\left({x}\right)\:+{cos}\:\left({x}\right)\right)}{{log}\:\left({sin}\left(\mathrm{2}{x}\right)\right)} \\ $$$$\:\:{find}\:\:\:{the}\:{Domain}\:{of}\:\:\:\:\mathrm{F}\:... \\ $$$$\:\:\:\mathrm{D}_{\:\mathrm{F}} \:=? \\ $$

Question Number 151208 Answers: 0 Comments: 0

Question Number 150967 Answers: 1 Comments: 0

E(x+(2/x))=((x^3 +1)/x) +((x^3 +8)/(2x^2 )) +3 , E(2)=?

$${E}\left({x}+\frac{\mathrm{2}}{{x}}\right)=\frac{{x}^{\mathrm{3}} +\mathrm{1}}{{x}}\:+\frac{{x}^{\mathrm{3}} +\mathrm{8}}{\mathrm{2}{x}^{\mathrm{2}} }\:+\mathrm{3}\:, \\ $$$$\:{E}\left(\mathrm{2}\right)=? \\ $$

Question Number 150742 Answers: 0 Comments: 0

Question Number 150626 Answers: 1 Comments: 0

S(x)=Σ_(n=1) ^∞ ln(1+(1/n))x^n S(−1)= ?.. please help..

$${S}\left({x}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right){x}^{{n}} \\ $$$${S}\left(−\mathrm{1}\right)=\:?.. \\ $$$${please}\:{help}.. \\ $$

Question Number 150171 Answers: 1 Comments: 0

solve in R: (((ax−b)^3 ))^(1/7) −(((b−ax)^(−3) ))^(1/7) =((65)/8)

$${solve}\:{in}\:\mathbb{R}: \\ $$$$\sqrt[{\mathrm{7}}]{\left({ax}−{b}\right)^{\mathrm{3}} }−\sqrt[{\mathrm{7}}]{\left({b}−{ax}\right)^{−\mathrm{3}} }=\frac{\mathrm{65}}{\mathrm{8}} \\ $$

Question Number 150044 Answers: 2 Comments: 0

Given f(((2x−3)/(2x+1)))+f(((2x+3)/(1−2x)))= 4x f(x)=?

$$\:\mathrm{Given}\:\mathrm{f}\left(\frac{\mathrm{2x}−\mathrm{3}}{\mathrm{2x}+\mathrm{1}}\right)+\mathrm{f}\left(\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{1}−\mathrm{2x}}\right)=\:\mathrm{4x} \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$

Question Number 149551 Answers: 1 Comments: 0

Question Number 148812 Answers: 1 Comments: 0

find ∫ (dx/(((√x)+(√(x+1)))((√(x−1))+(√x))))

$$\mathrm{find}\:\int\:\:\frac{\mathrm{dx}}{\left(\sqrt{\mathrm{x}}+\sqrt{\mathrm{x}+\mathrm{1}}\right)\left(\sqrt{\mathrm{x}−\mathrm{1}}+\sqrt{\mathrm{x}}\right)} \\ $$

Question Number 148568 Answers: 2 Comments: 0

calculate lim_(x→0) ((sh(2sinx)−sin(sh(2x)))/x^2 )

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\:\frac{\mathrm{sh}\left(\mathrm{2sinx}\right)−\mathrm{sin}\left(\mathrm{sh}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 148564 Answers: 1 Comments: 0

calculate ∫_1 ^2 ((logx)/(1+x))dx

$$\mathrm{calculate}\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\frac{\mathrm{logx}}{\mathrm{1}+\mathrm{x}}\mathrm{dx} \\ $$

Question Number 148558 Answers: 2 Comments: 0

Trouver toutes les fonctions continues f:R→R verifiant: ∀(x,y)∈R^2 , f(x+y)f(x−y)=f^2 (x)f^2 (y).. monsieur j′ai suppose^ que f est un morphisme mutiplicatif de R.. mais ca ne sort pas...

$$\mathrm{Trouver}\:\mathrm{toutes}\:\mathrm{les}\:\mathrm{fonctions}\:\mathrm{continues} \\ $$$$\mathrm{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{verifiant}: \\ $$$$\forall\left(\mathrm{x},\mathrm{y}\right)\in\mathbb{R}^{\mathrm{2}} ,\:\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)\mathrm{f}\left(\mathrm{x}−\mathrm{y}\right)=\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)\mathrm{f}^{\mathrm{2}} \left(\mathrm{y}\right).. \\ $$$$\mathrm{monsieur}\:\mathrm{j}'\mathrm{ai}\:\mathrm{suppos}\acute {\mathrm{e}}\:\mathrm{que}\:\mathrm{f}\:\mathrm{est}\:\mathrm{un}\: \\ $$$$\mathrm{morphisme}\:\mathrm{mutiplicatif}\:\mathrm{de}\:\mathbb{R}..\:\mathrm{mais}\:\mathrm{ca}\:\mathrm{ne} \\ $$$$\mathrm{sort}\:\mathrm{pas}... \\ $$

Question Number 148502 Answers: 3 Comments: 0

let α and β roots of x^2 +x+2 simplify Σ_(k=0) ^(n−1) (α^k +β^k ) and Σ_(k=0) ^(n−1) ( (1/α^k )+(1/β^k ))

$$\mathrm{let}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{roots}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{2} \\ $$$$\mathrm{simplify}\:\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}−\mathrm{1}} \:\:\left(\alpha^{\mathrm{k}} \:+\beta^{\mathrm{k}} \right)\:\:\mathrm{and}\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}−\mathrm{1}} \left(\:\frac{\mathrm{1}}{\alpha^{\mathrm{k}} }+\frac{\mathrm{1}}{\beta^{\mathrm{k}} }\right) \\ $$

Question Number 148501 Answers: 2 Comments: 0

let U_n ={z∈C /z^n =1} simplify Σ_(p=0) ^(2n−1) w^p with w∈U_n and Σ_(p=0) ^(2n−1) (2w +1)^p

$$\mathrm{let}\:\mathrm{U}_{\mathrm{n}} =\left\{\mathrm{z}\in\mathrm{C}\:/\mathrm{z}^{\mathrm{n}} \:=\mathrm{1}\right\}\:\:\mathrm{simplify} \\ $$$$\sum_{\mathrm{p}=\mathrm{0}} ^{\mathrm{2n}−\mathrm{1}} \:\mathrm{w}^{\mathrm{p}} \:\:\:\:\:\:\:\:\mathrm{with}\:\mathrm{w}\in\mathrm{U}_{\mathrm{n}} \:\:\: \\ $$$$\mathrm{and}\:\:\sum_{\mathrm{p}=\mathrm{0}} ^{\mathrm{2n}−\mathrm{1}} \left(\mathrm{2w}\:+\mathrm{1}\right)^{\mathrm{p}} \\ $$

Question Number 148498 Answers: 1 Comments: 0

find ∫_0 ^∞ ((arctan(2x))/(1+x^2 ))dx

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

Question Number 148372 Answers: 1 Comments: 0

calculate ∫_γ z^3 e^(1/z^2 ) dz with γ(t)=3e^(it) and t∈[0,2π]

$$\mathrm{calculate}\:\int_{\gamma} \mathrm{z}^{\mathrm{3}} \:\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{2}} }} \mathrm{dz}\:\:\mathrm{with}\:\gamma\left(\mathrm{t}\right)=\mathrm{3e}^{\mathrm{it}} \:\:\:\:\mathrm{and}\:\mathrm{t}\in\left[\mathrm{0},\mathrm{2}\pi\right] \\ $$

Question Number 148371 Answers: 1 Comments: 0

calculate ∫_γ ze^(2/z^2 ) dz with γ(t)=(√3)e^(it) t∈[0,2π]

$$\mathrm{calculate}\:\int_{\gamma} \mathrm{ze}^{\frac{\mathrm{2}}{\mathrm{z}^{\mathrm{2}} }} \mathrm{dz}\:\:\:\mathrm{with}\:\gamma\left(\mathrm{t}\right)=\sqrt{\mathrm{3}}\mathrm{e}^{\mathrm{it}} \:\:\:\:\:\:\mathrm{t}\in\left[\mathrm{0},\mathrm{2}\pi\right] \\ $$

Question Number 148303 Answers: 2 Comments: 0

f(x)=((cos(2x))/(sin(x))) developp f at fourier serie

$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{sin}\left(\mathrm{x}\right)} \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 148302 Answers: 2 Comments: 0

calculate ∫_(∣z∣=3) ((cos(2iz))/((z−2i)(z+i(√3))^2 ))dz

$$\mathrm{calculate}\:\:\int_{\mid\mathrm{z}\mid=\mathrm{3}} \:\:\:\frac{\mathrm{cos}\left(\mathrm{2iz}\right)}{\left(\mathrm{z}−\mathrm{2i}\right)\left(\mathrm{z}+\mathrm{i}\sqrt{\mathrm{3}}\right)^{\mathrm{2}} }\mathrm{dz} \\ $$

Question Number 148237 Answers: 1 Comments: 0

f(t)=sin(pt) fourier serie..

$${f}\left({t}\right)={sin}\left({pt}\right)\:{fourier}\:{serie}.. \\ $$

Question Number 148213 Answers: 1 Comments: 0

f(z)=((cosz)/(1−sin(z^2 ))) find residus of f

$$\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{cosz}}{\mathrm{1}−\mathrm{sin}\left(\mathrm{z}^{\mathrm{2}} \right)} \\ $$$$\mathrm{find}\:\mathrm{residus}\:\mathrm{of}\:\mathrm{f} \\ $$

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