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Question Number 39120 Answers: 1 Comments: 1

let A_n = ∫_1 ^n (([(√(1+x^2 ))] −[x])/x^2 ) dx (n integr ≥1) 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:{A}_{{n}} =\:\int_{\mathrm{1}} ^{{n}} \:\frac{\left[\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right]\:−\left[{x}\right]}{{x}^{\mathrm{2}} }\:{dx}\:\:\left({n}\:{integr}\:\geqslant\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \: \\ $$

Question Number 39119 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((x^2 cos(4x))/((x^2 +1)^2 ))dx

$${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}^{\mathrm{2}} \:{cos}\left(\mathrm{4}{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 39104 Answers: 1 Comments: 1

Question Number 39089 Answers: 2 Comments: 1

Question Number 39078 Answers: 1 Comments: 2

Without using l′hopital find lim_(x→3) ((√(9−x^2 ))/(x−3))

$$\boldsymbol{{Without}}\:\boldsymbol{{using}}\:\boldsymbol{{l}}'\boldsymbol{{hopital}} \\ $$$$\boldsymbol{{find}}\:\:\:\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{9}−\boldsymbol{{x}}^{\mathrm{2}} }}{\boldsymbol{{x}}−\mathrm{3}} \\ $$$$ \\ $$

Question Number 39072 Answers: 2 Comments: 1

Question Number 39067 Answers: 2 Comments: 7

Question Number 39059 Answers: 1 Comments: 0

Question Number 39058 Answers: 1 Comments: 1

Question Number 39055 Answers: 1 Comments: 0

Question Number 39040 Answers: 0 Comments: 0

find F(x) = ∫_0 ^π ln(x^2 −2x sin(2θ) +1)dθ .

$${find}\:{F}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left({x}^{\mathrm{2}} \:−\mathrm{2}{x}\:{sin}\left(\mathrm{2}\theta\right)\:+\mathrm{1}\right){d}\theta\:. \\ $$

Question Number 39039 Answers: 0 Comments: 2

let f(x) =(1/(1+∣sinx∣)) (2π periodic even) developp f at fourier serie .

$${let}\:{f}\left({x}\right)\:=\frac{\mathrm{1}}{\mathrm{1}+\mid{sinx}\mid}\:\:\:\left(\mathrm{2}\pi\:{periodic}\:{even}\right) \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$

Question Number 39038 Answers: 0 Comments: 2

let f(z) = (z/(z^2 −z+2)) developp f at integr serie.

$${let}\:{f}\left({z}\right)\:=\:\frac{{z}}{{z}^{\mathrm{2}} \:−{z}+\mathrm{2}} \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 39037 Answers: 0 Comments: 2

calculate F(x)=∫_0 ^(2π) ((cos(4t))/(x^2 −2x cost +1)) dt

$$\:{calculate}\:\:{F}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}\left(\mathrm{4}{t}\right)}{{x}^{\mathrm{2}} \:−\mathrm{2}{x}\:{cost}\:+\mathrm{1}}\:{dt} \\ $$

Question Number 39035 Answers: 0 Comments: 1

find f(t) =∫_0 ^∞ sin(x)e^(−t [x]) dx with t>0

$${find}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:{sin}\left({x}\right){e}^{−{t}\:\left[{x}\right]} {dx}\:\:\:{with}\:{t}>\mathrm{0} \\ $$

Question Number 39034 Answers: 0 Comments: 1

calculate interms of n A_n = ∫_0 ^(2π) ((cos(nx))/(cosx +sinx))dx and B_n = ∫_0 ^(2π) ((sin(nx))/(cosx +sinx))dx .

$${calculate}\:{interms}\:{of}\:{n} \\ $$$${A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}\left({nx}\right)}{{cosx}\:+{sinx}}{dx}\:\:{and}\:{B}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{sin}\left({nx}\right)}{{cosx}\:+{sinx}}{dx}\:. \\ $$

Question Number 39033 Answers: 0 Comments: 2

calculate ∫_(−∞) ^(+∞) ((xsin(2x))/((1+x^2 )^2 ))dx

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

Question Number 39032 Answers: 1 Comments: 0

x+y=3 x=2 y=?

$${x}+{y}=\mathrm{3} \\ $$$${x}=\mathrm{2} \\ $$$${y}=? \\ $$

Question Number 39028 Answers: 1 Comments: 0

1) calculate A=cos((π/7)).cos(((2π)/7)).cos(((3π)/7)) 2) calculate B =tan((π/7)).tan(((2π)/7)).tan(((3π)/7)).

$$\left.\mathrm{1}\right)\:{calculate}\:\:{A}={cos}\left(\frac{\pi}{\mathrm{7}}\right).{cos}\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right).{cos}\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{B}\:={tan}\left(\frac{\pi}{\mathrm{7}}\right).{tan}\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right).{tan}\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right). \\ $$

Question Number 39026 Answers: 2 Comments: 0

find the roots of 8x^3 −4x−1 =0

$${find}\:{the}\:{roots}\:{of}\:\:\mathrm{8}{x}^{\mathrm{3}} \:−\mathrm{4}{x}−\mathrm{1}\:=\mathrm{0} \\ $$

Question Number 39025 Answers: 0 Comments: 1

let f(x)= ((cos(αx))/(cosx)) (2π periodic even) developp f at fourier serie.

$${let}\:{f}\left({x}\right)=\:\frac{{cos}\left(\alpha{x}\right)}{{cosx}}\:\:\:\:\left(\mathrm{2}\pi\:{periodic}\:{even}\right) \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}. \\ $$

Question Number 39024 Answers: 0 Comments: 2

find the value of I = ∫_0 ^1 ((arctan(2x))/(√(1+4x^2 ))) dx

$${find}\:{the}\:{value}\:{of}\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\sqrt{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }}\:{dx} \\ $$

Question Number 39023 Answers: 0 Comments: 1

let g(x)= ∫_(−∞) ^(+∞) ((arctan(x(1+t^2 )))/(1+t^2 ))dt with x>0 find a simple form of g(x) .

$${let}\:{g}\left({x}\right)=\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{arctan}\left({x}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:\:\:{with}\:{x}>\mathrm{0} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{g}\left({x}\right)\:. \\ $$

Question Number 39022 Answers: 0 Comments: 1

let p(x)= (1+e^(iθ) x)^n −(1−e^(iθ) x)^n with n integr natural 1) find the roots of p(x) 2) fctorize inside C[x] p(x) 3) factorize inside R[x] p(x). θ ∈R

$${let}\:{p}\left({x}\right)=\:\left(\mathrm{1}+{e}^{{i}\theta} {x}\right)^{{n}} \:−\left(\mathrm{1}−{e}^{{i}\theta} {x}\right)^{{n}} \:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{fctorize}\:{inside}\:{C}\left[{x}\right]\:{p}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{factorize}\:{inside}\:{R}\left[{x}\right]\:{p}\left({x}\right).\:\:\theta\:\in{R} \\ $$

Question Number 39021 Answers: 0 Comments: 0

calculate A_n = ∫_0 ^1 sin(narctanx)dx with n integr natural. 2) find nature of Σ_n A_n

$${calculate}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{sin}\left({narctanx}\right){dx}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\sum_{{n}} \:\:{A}_{{n}} \\ $$

Question Number 39020 Answers: 1 Comments: 0

calculate ∫_0 ^1 ((ln(1+(√(x^2 +1))))/(√(x^2 +1))) dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}+\sqrt{{x}^{\mathrm{2}} \:+\mathrm{1}}\right)}{\sqrt{{x}^{\mathrm{2}} \:+\mathrm{1}}}\:{dx} \\ $$

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