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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

Question Number 65277 Answers: 0 Comments: 1

Question Number 65276 Answers: 0 Comments: 1

Question Number 65271 Answers: 1 Comments: 0

x^4 +ax^2 +bx+c=0 solve for x.

$${x}^{\mathrm{4}} +{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$${solve}\:{for}\:{x}. \\ $$

Question Number 65270 Answers: 1 Comments: 0

d/dx x−2

$${d}/{dx}\:{x}−\mathrm{2} \\ $$

Question Number 65269 Answers: 0 Comments: 0

Question Number 65261 Answers: 0 Comments: 1

solve4−xy+yz−xz

$${solve}\mathrm{4}−{xy}+{yz}−{xz} \\ $$

Question Number 65239 Answers: 1 Comments: 8

Question Number 65235 Answers: 1 Comments: 2

Question Number 65227 Answers: 0 Comments: 3

Question Number 65219 Answers: 1 Comments: 1

Question Number 65217 Answers: 0 Comments: 1

Question Number 65214 Answers: 1 Comments: 3

Prove or disprove that 2^(101) ∣ n^n − 101 .

$${Prove}\:\:{or}\:\:{disprove}\:\:\:{that}\:\:\:\mathrm{2}^{\mathrm{101}} \:\mid\:{n}^{{n}} \:−\:\mathrm{101}\:. \\ $$

Question Number 65212 Answers: 1 Comments: 1

Question Number 65203 Answers: 1 Comments: 1

∫_0 ^∞ (x^2 /(x^4 +x^2 +1))dx

$$\int_{\mathrm{0}} ^{\infty} \:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 65202 Answers: 1 Comments: 0

∫_0 ^π ((cos 2θ)/(1−2acos θ+a^2 ))dθ, a^2 <1 answer?

$$\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{cos}\:\mathrm{2}\theta}{\mathrm{1}−\mathrm{2}{a}\mathrm{cos}\:\theta+{a}^{\mathrm{2}} }{d}\theta,\:{a}^{\mathrm{2}} <\mathrm{1} \\ $$$$\mathrm{answer}? \\ $$

Question Number 65200 Answers: 2 Comments: 0

Question Number 65199 Answers: 1 Comments: 0

Question Number 65198 Answers: 0 Comments: 5

let a∈R^+ , and x>0 x^4 +(1−2a)x^2 −2ax+1=0 find x

$${let}\:{a}\in\mathbb{R}^{+} \:,\:{and}\:{x}>\mathrm{0} \\ $$$${x}^{\mathrm{4}} +\left(\mathrm{1}−\mathrm{2}{a}\right){x}^{\mathrm{2}} −\mathrm{2}{ax}+\mathrm{1}=\mathrm{0} \\ $$$${find}\:{x} \\ $$

Question Number 65196 Answers: 0 Comments: 0

find ∫_0 ^1 ((1/(1−x)) +(1/(lnx)))dx

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

Question Number 65195 Answers: 0 Comments: 0

find ∫_(π/4) ^(π/2) ln(ln(tanx)dx

$${find}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left({ln}\left({tanx}\right){dx}\right. \\ $$

Question Number 65194 Answers: 0 Comments: 0

calculate ∫_0 ^1 ln(Γ(x))dx with Γ(x) =∫_0 ^∞ t^(x−1) e^(−t) dt and x>0

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\Gamma\left({x}\right)\right){dx}\:{with}\:\Gamma\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\:\:{and}\:{x}>\mathrm{0} \\ $$

Question Number 65193 Answers: 0 Comments: 1

U_n is a sequence wich verify U_n +U_(n+1) =n for all integr n 1) calculate U_n intrem of n 2) find nature of the serie Σ (U_n /n^2 )

$${U}_{{n}} \:{is}\:{a}\:{sequence}\:{wich}\:{verify}\:{U}_{{n}} +{U}_{{n}+\mathrm{1}} ={n}\:{for}\:{all}\:{integr}\:{n} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{intrem}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:\frac{{U}_{{n}} }{{n}^{\mathrm{2}} } \\ $$

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