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Question Number 62828 Answers: 0 Comments: 1

let U_n =∫_0 ^(+∞) ((cos(ch(nx)))/((3+x^2 )^2 ))dx 1) calculate U_n interms of n 2) find lim_(n→+∞) n U_n and lim_(n→+∞) n^2 U_n 3)study the serie Σ U_n

$${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{cos}\left({ch}\left({nx}\right)\right)}{\left(\mathrm{3}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{U}_{{n}} \:\:\:\:\:{and}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{\mathrm{2}} \:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{serie}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 62826 Answers: 0 Comments: 4

Question Number 62821 Answers: 2 Comments: 1

Question Number 62815 Answers: 0 Comments: 2

developp at fourier serie f(x) =cos(tx) ,2π periodic even .

$${developp}\:{at}\:{fourier}\:{serie}\:{f}\left({x}\right)\:={cos}\left({tx}\right)\:\:,\mathrm{2}\pi\:{periodic}\:{even}\:. \\ $$

Question Number 62814 Answers: 0 Comments: 10

Question Number 62813 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ e^(−(t^2 +(1/t^2 ))) dt study first the convergence .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left({t}^{\mathrm{2}} \:+\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right)} {dt} \\ $$$${study}\:{first}\:{the}\:{convergence}\:. \\ $$

Question Number 62812 Answers: 0 Comments: 1

let U_n =∫_0 ^(+∞) ((arctan(nt))/(1+n^2 t^2 ))dt with n natural≥1 1) calculate U_n 2) calculate lim_(n→+∞) n^2 U_n 3) study the convergence of Σ U_n

$${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{arctan}\left({nt}\right)}{\mathrm{1}+{n}^{\mathrm{2}} {t}^{\mathrm{2}} }{dt}\:\:\:\:{with}\:{n}\:{natural}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{\mathrm{2}} \:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 62811 Answers: 0 Comments: 2

1) find ∫ ((2x^2 −1)/((x+1)(x−3)(x^2 −x+2)))dx 2)calculate ∫_5 ^(+∞) ((2x^2 −1)/((x+1)(x−3)(x^2 −x+2)))dx

$$\left.\mathrm{1}\right)\:{find}\:\:\int\:\:\:\frac{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{3}\right)\left({x}^{\mathrm{2}} −{x}+\mathrm{2}\right)}{dx} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{5}} ^{+\infty} \:\:\:\:\frac{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{3}\right)\left({x}^{\mathrm{2}} −{x}+\mathrm{2}\right)}{dx} \\ $$

Question Number 62809 Answers: 0 Comments: 1

let f(x) = arctan(nx) with n integr natural 1) calculate f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie .

$${let}\:{f}\left({x}\right)\:=\:{arctan}\left({nx}\right)\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 62808 Answers: 0 Comments: 0

f(t) =∫_0 ^(+∞) (e^(−xt) /((x+t)^2 ))dx with t≥0 1) study the set of definition for f(t) 2)study the continuity of f 3)study the derivability of f 4) developp f at integr serie

$${f}\left({t}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{e}^{−{xt}} }{\left({x}+{t}\right)^{\mathrm{2}} }{dx}\:\:\:\:{with}\:{t}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{set}\:{of}\:{definition}\:{for}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{continuity}\:{of}\:{f} \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{derivability}\:{of}\:{f} \\ $$$$\left.\mathrm{4}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 62806 Answers: 0 Comments: 1

find the value of ∫_(−∞) ^(+∞) ((x+1)/((x^4 +x^2 +1)^3 ))dx

$${find}\:{the}\:{value}\:{of}\:\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}+\mathrm{1}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$

Question Number 62805 Answers: 0 Comments: 1

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

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

Question Number 63060 Answers: 1 Comments: 0

Question Number 62801 Answers: 0 Comments: 0

Question Number 62800 Answers: 0 Comments: 2

Question Number 62798 Answers: 0 Comments: 0

Calculate tg(20°)+4sin(20°)+1

$$\boldsymbol{\mathrm{Calculate}} \\ $$$$\boldsymbol{\mathrm{tg}}\left(\mathrm{20}°\right)+\mathrm{4}\boldsymbol{\mathrm{sin}}\left(\mathrm{20}°\right)+\mathrm{1} \\ $$

Question Number 62790 Answers: 1 Comments: 1

Question Number 62782 Answers: 0 Comments: 0

Question Number 62781 Answers: 0 Comments: 0

∫ sec(2x) e^(2x) dx

$$\int\:\mathrm{sec}\left(\mathrm{2x}\right)\:\mathrm{e}^{\mathrm{2x}} \:\:\mathrm{dx} \\ $$

Question Number 62777 Answers: 0 Comments: 1

5^(3x−1) .4^(2x−2) =625

$$\mathrm{5}^{\mathrm{3}{x}−\mathrm{1}} .\mathrm{4}^{\mathrm{2}{x}−\mathrm{2}} =\mathrm{625} \\ $$

Question Number 62763 Answers: 0 Comments: 0

Question Number 62762 Answers: 0 Comments: 0

Question Number 62761 Answers: 0 Comments: 3

if cosθ=((cosA.cosB)/(1−cosA.cosB)) prove that Tan(θ/2)=Tan(A/2).Cot(B/2)

$$\mathrm{if}\:\mathrm{cos}\theta=\frac{\mathrm{cosA}.\mathrm{cosB}}{\mathrm{1}−\mathrm{cosA}.\mathrm{cosB}}\:\:\:\mathrm{prove}\:\mathrm{that}\:\mathrm{Tan}\frac{\theta}{\mathrm{2}}=\mathrm{Tan}\frac{\mathrm{A}}{\mathrm{2}}.\mathrm{Cot}\frac{\mathrm{B}}{\mathrm{2}} \\ $$

Question Number 62759 Answers: 1 Comments: 0

y = x^y (dy/dx) = ?

$${y}\:\:=\:\:{x}^{{y}} \\ $$$$\frac{{dy}}{{dx}}\:\:=\:\:? \\ $$

Question Number 62754 Answers: 1 Comments: 2

1)∫(dx/(1−sin(x))) R solve in(2) (4−x)^4 +x^4 =82

$$\left.\mathrm{1}\right)\int\frac{{dx}}{\mathrm{1}−{sin}\left({x}\right)} \\ $$$$ \\ $$$${R}\:{solve}\:{in}\left(\mathrm{2}\right) \\ $$$$ \\ $$$$\left(\mathrm{4}−{x}\right)^{\mathrm{4}} +{x}^{\mathrm{4}} =\mathrm{82} \\ $$

Question Number 62753 Answers: 1 Comments: 0

The normal at the point P(4cos θ,3sin θ) on the ellipse (x^2 /(16)) +(y^2 /9)=1 meets the x−axis and y−axis at A and B respectively show that locus of the mid−point of AB is an ellipse with the same eccentricity as given ellipse.

$${The}\:{normal}\:{at}\:{the}\:{point} \\ $$$${P}\left(\mathrm{4cos}\:\theta,\mathrm{3sin}\:\theta\right)\:{on}\:{the} \\ $$$${ellipse}\:\frac{{x}^{\mathrm{2}} }{\mathrm{16}}\:+\frac{{y}^{\mathrm{2}} }{\mathrm{9}}=\mathrm{1}\:{meets} \\ $$$${the}\:{x}−{axis}\:{and}\:{y}−{axis} \\ $$$${at}\:{A}\:{and}\:{B}\:{respectively} \\ $$$${show}\:{that}\:{locus}\:{of}\:{the} \\ $$$${mid}−{point}\:{of}\:{AB}\:{is}\:{an} \\ $$$${ellipse}\:{with}\:{the}\:{same} \\ $$$${eccentricity}\:{as}\:{given} \\ $$$${ellipse}. \\ $$

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