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AllQuestion and Answers: Page 1703

Question Number 37296 Answers: 0 Comments: 1

solve sinz =2 zfromC

$${solve}\:{sinz}\:=\mathrm{2}\:\:\:\:\:{zfromC} \\ $$$$ \\ $$

Question Number 37295 Answers: 0 Comments: 0

find the principal value of{(1+i)^(1−i) }^(1+i) .

$${find}\:{the}\:{principal}\:{value}\:{of}\left\{\left(\mathrm{1}+{i}\right)^{\mathrm{1}−{i}} \right\}^{\mathrm{1}+{i}} . \\ $$

Question Number 37294 Answers: 0 Comments: 0

let D =D(0,1) and f(z) =Σ_(n=0) ^∞ a_n z^n is a holomorphe function / ∣f(x)∣< (1/(1−∣z∣)) prove that ∣a_n ∣≤ (n+1)(1+(1/n))^n ≤(n+1)e.

$${let}\:{D}\:={D}\left(\mathrm{0},\mathrm{1}\right)\:{and}\:{f}\left({z}\right)\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:{a}_{{n}} {z}^{{n}} \:{is}\:{a}\:{holomorphe} \\ $$$${function}\:/\:\:\mid{f}\left({x}\right)\mid<\:\:\frac{\mathrm{1}}{\mathrm{1}−\mid{z}\mid}\:\:{prove}\:{that} \\ $$$$\mid{a}_{{n}} \mid\leqslant\:\left({n}+\mathrm{1}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} \leqslant\left({n}+\mathrm{1}\right){e}. \\ $$

Question Number 37291 Answers: 0 Comments: 1

calculate g(θ) = ∫_(−∞) ^(+∞) e^(−x^2 ) sin(sinθ x^2 )dx .

$${calculate}\:{g}\left(\theta\right)\:=\:\int_{−\infty} ^{+\infty} \:{e}^{−{x}^{\mathrm{2}} } \:{sin}\left({sin}\theta\:{x}^{\mathrm{2}} \right){dx}\:. \\ $$

Question Number 37290 Answers: 0 Comments: 0

find f(θ) = ∫_(−∞) ^(+∞) e^(−x^2 ) cos(cosθx)dx .

$${find}\:\:{f}\left(\theta\right)\:=\:\int_{−\infty} ^{+\infty} \:{e}^{−{x}^{\mathrm{2}} } \:{cos}\left({cos}\theta{x}\right){dx}\:. \\ $$

Question Number 37289 Answers: 0 Comments: 0

calculate ∫_0 ^(2π) (dx/(cos^2 t +4sin^2 t))dt .

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\:\:\frac{{dx}}{{cos}^{\mathrm{2}} {t}\:\:+\mathrm{4}{sin}^{\mathrm{2}} {t}}{dt}\:. \\ $$

Question Number 37288 Answers: 0 Comments: 1

calculate f(α) = ∫_(−∞) ^(+∞) ((cos(2x))/(1+ax^2 )) dx with a>0 2) find the value of ∫_(−∞) ^(+∞) ((cos(2x))/(1+3x^2 )) dx .

$${calculate}\:\:{f}\left(\alpha\right)\:=\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{ax}^{\mathrm{2}} }\:{dx}\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{3}{x}^{\mathrm{2}} }\:{dx}\:. \\ $$

Question Number 37287 Answers: 0 Comments: 1

calculate f(t) = ∫_(−∞) ^(+∞) ((cos(tx))/(1+x^2 )) dx

$${calculate}\:\:{f}\left({t}\right)\:=\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left({tx}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 37285 Answers: 0 Comments: 3

let A_n = ∫_0 ^∞ e^(−nx^2 ) sin((x/n))dx with n integr not 0 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{nx}^{\mathrm{2}} } {sin}\left(\frac{{x}}{{n}}\right){dx}\:\:{with}\:{n}\:{integr}\:{not}\:\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 37284 Answers: 0 Comments: 1

find A_n = ∫_0 ^1 (x^n /(ch(x))) dx .

$${find}\:\:{A}_{{n}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}^{{n}} }{{ch}\left({x}\right)}\:{dx}\:. \\ $$

Question Number 37283 Answers: 0 Comments: 1

find ∫_0 ^∞ ((cosx)/(ch(x))) dx .

$${find}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{cosx}}{{ch}\left({x}\right)}\:{dx}\:. \\ $$

Question Number 37282 Answers: 0 Comments: 5

let f(x)=(x/(1+x^2 +x^4 )) 1) find f^((n)) (x) 2)calculate f^((n)) (0) 3)developp f at integr serie.

$${let}\:{f}\left({x}\right)=\frac{{x}}{\mathrm{1}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right){developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 37281 Answers: 0 Comments: 1

find a better approximation for the integrals 1) ∫_0 ^1 e^(−x^2 ) dx 2) ∫_1 ^(+∞) e^(−x^2 ) dx .

$${find}\:{a}\:{better}\:{approximation}\:{for}\:{the} \\ $$$${integrals}\: \\ $$$$\left.\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{e}^{−{x}^{\mathrm{2}} } {dx} \\ $$$$\left.\mathrm{2}\right)\:\int_{\mathrm{1}} ^{+\infty} \:{e}^{−{x}^{\mathrm{2}} } {dx}\:. \\ $$

Question Number 37280 Answers: 0 Comments: 1

calculate ∫_0 ^6 (e^(x−[x]) /(1+e^x ))dx .

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{6}} \:\:\:\frac{{e}^{{x}−\left[{x}\right]} }{\mathrm{1}+{e}^{{x}} }{dx}\:. \\ $$

Question Number 37279 Answers: 1 Comments: 1

cslculate ∫∫_([0,1]^2 ) (x−y)e^(−x−y) dxdy .

$${cslculate}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\left({x}−{y}\right){e}^{−{x}−{y}} {dxdy}\:. \\ $$

Question Number 37278 Answers: 0 Comments: 1

calculate ∫∫_D x cos(x^2 +y^2 )dxdy with D={(x,y)∈R^2 / 0≤x≤1 and 1≤y≤3}

$$\:{calculate}\:\int\int_{{D}} \:{x}\:{cos}\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right){dxdy} \\ $$$${with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\right. \\ $$$$\left.\mathrm{1}\leqslant{y}\leqslant\mathrm{3}\right\} \\ $$

Question Number 37277 Answers: 0 Comments: 3

let f(x) = (1/(1+x^n )) with n integr 1)find f^′ (x) and f^(′′) (x) 2) find the poles of f 3)calculate f^((n)) (0) 4) developp f at integr serie.

$${let}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{{n}} }\:\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right){find}\:{f}^{'} \left({x}\right)\:{and}\:{f}^{''} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{poles}\:{of}\:{f} \\ $$$$\left.\mathrm{3}\right){calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{4}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 37276 Answers: 0 Comments: 0

calculate I_n =∫_0 ^4 (−1)^([x]) (x^n −x)dx

$${calculate}\:\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{4}} \:\left(−\mathrm{1}\right)^{\left[{x}\right]} \left({x}^{{n}} \:−{x}\right){dx} \\ $$

Question Number 37275 Answers: 0 Comments: 0

let A_n = ∫_0 ^(1/n) arctan(1+x^2 )dx 1) calculate A_n 2)find lim_(n→+∞) A_n .

$${let}\:{A}_{{n}} \:=\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{{n}}} \:{arctan}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \:. \\ $$

Question Number 37273 Answers: 0 Comments: 0

let f(x)=ln(x−sinx) 1)find D_f 2)developp f at integr serie.

$${let}\:{f}\left({x}\right)={ln}\left({x}−{sinx}\right) \\ $$$$\left.\mathrm{1}\right){find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 37272 Answers: 0 Comments: 0

let f(x)=cos(x−e^(−x) ) developp f at integr serie.

$${let}\:{f}\left({x}\right)={cos}\left({x}−{e}^{−{x}} \right) \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 37271 Answers: 0 Comments: 2

find A_n =∫_1 ^2 ( 1 +(1/x) +(1/x^2 ) +...+(1/x^n ))^2 dx

$${find}\:\:{A}_{{n}} =\int_{\mathrm{1}} ^{\mathrm{2}} \left(\:\mathrm{1}\:+\frac{\mathrm{1}}{{x}}\:+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:+...+\frac{\mathrm{1}}{{x}^{{n}} }\right)^{\mathrm{2}} {dx} \\ $$

Question Number 37270 Answers: 1 Comments: 0

find ∫_0 ^1 (((1−x^(n+1) )/(1−x)))^2 dx .

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

Question Number 37269 Answers: 0 Comments: 2

let f(x)= e^(−2x) ln(1+x) developp f at integr serie .

$${let}\:{f}\left({x}\right)=\:{e}^{−\mathrm{2}{x}} {ln}\left(\mathrm{1}+{x}\right) \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 37263 Answers: 1 Comments: 1

Question Number 37258 Answers: 1 Comments: 0

∫ ((x^3 +1)/(√(x^2 +x))) dx = ?

$$\int\:\frac{{x}^{\mathrm{3}} +\mathrm{1}}{\sqrt{{x}^{\mathrm{2}} +{x}}}\:{dx}\:=\:? \\ $$

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