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Question Number 65320 Answers: 0 Comments: 1

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Question Number 65297 Answers: 0 Comments: 1

let U_n a sequence wich verify U_n +U_(n+1) +U_(n+2) =n(−1)^n for all integr n calculate interms of n A_n =Σ_(k=0) ^n (−1)^k U_k the first term is U_0

$${let}\:\:\:{U}_{{n}} \:\:{a}\:{sequence}\:{wich}\:{verify}\:\:{U}_{{n}} \:+{U}_{{n}+\mathrm{1}} +{U}_{{n}+\mathrm{2}} \:={n}\left(−\mathrm{1}\right)^{{n}} \\ $$$${for}\:{all}\:{integr}\:{n}\:\:\:{calculate}\:{interms}\:{of}\:{n} \\ $$$${A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\left(−\mathrm{1}\right)^{{k}} \:{U}_{{k}} \\ $$$${the}\:{first}\:{term}\:{is}\:{U}_{\mathrm{0}} \\ $$

Question Number 65293 Answers: 0 Comments: 3

1) calculate ∫_(−∞) ^(+∞) (dx/(x−a)) with a ∈C 2) find the values of ∫_0 ^∞ (dx/(x^4 +1)) and ∫_0 ^∞ (dx/(x^6 +1)) by using the decomposition inside C(x).

$$\left.\mathrm{1}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}−{a}}\:\:{with}\:{a}\:\in{C} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}}\:\:{and}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{6}} \:+\mathrm{1}} \\ $$$${by}\:{using}\:{the}\:{decomposition}\:{inside}\:{C}\left({x}\right). \\ $$

Question Number 65292 Answers: 0 Comments: 0

Question Number 65290 Answers: 1 Comments: 3

f(x) =∫_0 ^1 (dt/(x+e^t )) with 0≤x≤1 1) find aexplicit form of f(x) 2) calculate ∫_0 ^1 (dt/(2+e^t )) 3) find g(x) =∫_0 ^1 (dt/((x+e^t )^2 )) 4) calculate ∫_0 ^1 (dt/((1+e^t )^2 )) 5) give f^((n)) (x) at form of integrals 6) developp f at integr serie.

$${f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{{x}+{e}^{{t}} }\:\:\:{with}\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{aexplicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{2}+{e}^{{t}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dt}}{\left({x}+{e}^{{t}} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\left(\mathrm{1}+{e}^{{t}} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{5}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integrals} \\ $$$$\left.\mathrm{6}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 65289 Answers: 1 Comments: 1

Question Number 65288 Answers: 0 Comments: 4

1) let f(x) =∫_0 ^(+∞) (dt/(t^3 +x^3 )) with x>0 calculate f(x) 2) find also g(x) =∫_0 ^∞ (dt/((t^3 +x^3 )^2 )) 3) find the values of integrals ∫_0 ^∞ (dt/(t^3 +1)) and ∫_0 ^∞ (dt/((t^3 +1)^2 )) 4) give f^((n)) (x) at form of integrals.

$$\left.\mathrm{1}\right)\:{let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{{t}^{\mathrm{3}} \:+{x}^{\mathrm{3}} }\:\:\:{with}\:{x}>\mathrm{0} \\ $$$${calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{3}} \:+{x}^{\mathrm{3}} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{{t}^{\mathrm{3}} \:+\mathrm{1}}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \frac{{dt}}{\left({t}^{\mathrm{3}} \:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{4}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integrals}. \\ $$

Question Number 65287 Answers: 0 Comments: 1

let f(x) =x∣x∣ 2π periodic odd developp f at fourier series

$${let}\:{f}\left({x}\right)\:={x}\mid{x}\mid\:\:\:\:\mathrm{2}\pi\:{periodic}\:\:{odd} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{series} \\ $$

Question Number 65286 Answers: 0 Comments: 2

1)find f(a)=∫_(−∞) ^(+∞) e^(−ax^2 ) cos(3−x^2 )dx with a>0 2) find the value of ∫_0 ^∞ e^(−3x^2 ) cos(3−x^2 )dx

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

Question Number 65285 Answers: 0 Comments: 1

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

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

Question Number 65281 Answers: 1 Comments: 1