Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1763

Question Number 30581    Answers: 0   Comments: 0

decompose inside C[x] F= (1/((x+iy)^n )) .

$${decompose}\:{inside}\:{C}\left[{x}\right]\:{F}=\:\:\frac{\mathrm{1}}{\left({x}+{iy}\right)^{{n}} }\:. \\ $$

Question Number 30580    Answers: 0   Comments: 1

decompose inside C[x] F= (x^n /(x^m +1)) with m≥n+2 then find ∫_0 ^∞ (x^n /(x^m +1))dx.

$${decompose}\:{inside}\:{C}\left[{x}\right]\:{F}=\:\frac{{x}^{{n}} }{{x}^{{m}} \:+\mathrm{1}}\:{with}\:{m}\geqslant{n}+\mathrm{2} \\ $$$${then}\:{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{{n}} }{{x}^{{m}} \:+\mathrm{1}}{dx}. \\ $$

Question Number 30579    Answers: 0   Comments: 0

decompose inside C[x] F= ((x^n −1)/(x^(2n) −1)) .

$${decompose}\:{inside}\:{C}\left[{x}\right]\:{F}=\:\frac{{x}^{{n}} −\mathrm{1}}{{x}^{\mathrm{2}{n}} −\mathrm{1}}\:. \\ $$

Question Number 30578    Answers: 0   Comments: 0

decompose F(x)= (1/((x^2 +1)^n )) on C[x].with n fromN.

$${decompose}\:{F}\left({x}\right)=\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{{n}} }\:{on}\:{C}\left[{x}\right].{with}\:{n}\:{fromN}. \\ $$

Question Number 30576    Answers: 0   Comments: 1

let consider the equation x^3 +px +q find S= Σ_(i≠j) (x_i /x_j ) .

$${let}\:{consider}\:{the}\:{equation}\:{x}^{\mathrm{3}} \:+{px}\:+{q}\: \\ $$$${find}\:{S}=\:\sum_{{i}\neq{j}} \:\frac{{x}_{{i}} }{{x}_{{j}} }\:. \\ $$

Question Number 30575    Answers: 0   Comments: 0

find ∫∫_D (x^2 +y^2 )dxdy with D={(x,y)/ x≤1 and x^2 ≤y≤2 }.

$${find}\:\int\int_{{D}} \:\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right){dxdy}\:\:{with} \\ $$$${D}=\left\{\left({x},{y}\right)/\:{x}\leqslant\mathrm{1}\:{and}\:{x}^{\mathrm{2}} \leqslant{y}\leqslant\mathrm{2}\:\right\}. \\ $$

Question Number 30574    Answers: 0   Comments: 0

find ∫∫_([1,e]^2 ) ln(xy)dxdy.

$${find}\:\int\int_{\left[\mathrm{1},{e}\right]^{\mathrm{2}} } \:\:\:{ln}\left({xy}\right){dxdy}. \\ $$

Question Number 30573    Answers: 0   Comments: 0

find ∫∫_([0,1]×[0,1]) (x^2 /(1+y^2 ))dxdy.

$${find}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},\mathrm{1}\right]} \:\:\:\:\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{y}^{\mathrm{2}} }{dxdy}. \\ $$

Question Number 30572    Answers: 0   Comments: 1

find I=∫∫_([3,4]×[1,2]) ((dxdy)/((x+y)^2 )) .

$${find}\:\:{I}=\int\int_{\left[\mathrm{3},\mathrm{4}\right]×\left[\mathrm{1},\mathrm{2}\right]} \:\:\frac{{dxdy}}{\left({x}+{y}\right)^{\mathrm{2}} }\:. \\ $$

Question Number 30571    Answers: 0   Comments: 0

decompose F(x)= (1/((1+x+x^2 )^n )) on C[x].

$${decompose}\:{F}\left({x}\right)=\:\frac{\mathrm{1}}{\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right)^{{n}} }\:{on}\:{C}\left[{x}\right]. \\ $$

Question Number 30570    Answers: 0   Comments: 0

find ∫∫_U ((dxdy)/(x^2 +y^2 )) with U= {(x,y)∈R^2 /1≤x^2 +2y^2 ≤4}

$${find}\:\int\int_{{U}} \:\frac{{dxdy}}{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }\:{with}\:{U}=\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{1}\leqslant{x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \leqslant\mathrm{4}\right\} \\ $$

Question Number 30569    Answers: 0   Comments: 0

find I= ∫∫_D (√(1−(x^2 /a^2 )−(y^2 /b^2 ))) dxdy with D is the interior of ellipce (x^2 /a^2 ) +(y^2 /b^2 ) =1.

$${find}\:{I}=\:\int\int_{{D}} \:\sqrt{\mathrm{1}−\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }−\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }}\:\:{dxdy}\:\:{with}\:{D}\:{is}\:{the}\:{interior} \\ $$$${of}\:{ellipce}\:\:\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:=\mathrm{1}. \\ $$

Question Number 30568    Answers: 0   Comments: 0

find ∫_(−1) ^1 (dx/((√(1+x^2 )) +(√(1−x^2 )))) .

$${find}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}}\:. \\ $$

Question Number 30567    Answers: 0   Comments: 0

integrate xy^, +(x−1)y +y^2 =0

$${integrate}\:{xy}^{,} \:+\left({x}−\mathrm{1}\right){y}\:+{y}^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 30566    Answers: 0   Comments: 0

study the convergence of A(α) =∫_0 ^∞ (t^(α−1) /(1+t^2 ))dt and find its value.

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

Question Number 30565    Answers: 0   Comments: 0

let f(x)= (1/(n!))(px−qx^2 )^n find maxf .

$${let}\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{{n}!}\left({px}−{qx}^{\mathrm{2}} \right)^{{n}} \:\:\:{find}\:{maxf}\:\:. \\ $$

Question Number 30564    Answers: 0   Comments: 0

f and g are 2 function C^n on [a,b] prove that ∫_a ^b f^((n)) (x)g(x)dx=[Σ_(k=0) ^(n−1) (−1)^k f^((k)) g^((n−k)) ]_a ^b +(−1)^n ∫_a ^b f(x)g^((n)) (x)dx

$${f}\:{and}\:{g}\:{are}\:\mathrm{2}\:{function}\:\:{C}^{{n}} \:{on}\:\left[{a},{b}\right]\:{prove}\:{that} \\ $$$$\int_{{a}} ^{{b}} \:{f}^{\left({n}\right)} \left({x}\right){g}\left({x}\right){dx}=\left[\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left(−\mathrm{1}\right)^{{k}} \:{f}^{\left({k}\right)} {g}^{\left({n}−{k}\right)} \right]_{{a}} ^{{b}} \:+\left(−\mathrm{1}\right)^{{n}} \int_{{a}} ^{{b}} {f}\left({x}\right){g}^{\left({n}\right)} \left({x}\right){dx} \\ $$

Question Number 30563    Answers: 0   Comments: 0

let f(x)=∣x−2 [((x+1)/2)]∣ 1) prove that f is periodic 2) simplify f(x) if p≤x+1 and p∈Z .

$${let}\:{f}\left({x}\right)=\mid{x}−\mathrm{2}\:\left[\frac{{x}+\mathrm{1}}{\mathrm{2}}\right]\mid \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{f}\:{is}\:{periodic} \\ $$$$\left.\mathrm{2}\right)\:{simplify}\:{f}\left({x}\right)\:{if}\:{p}\leqslant{x}+\mathrm{1}\:{and}\:{p}\in{Z}\:. \\ $$

Question Number 30560    Answers: 0   Comments: 0

study the roots of f_n (x)= Σ_(k=0) ^n (x^k /(k!)) .

$${study}\:{the}\:{roots}\:{of}\:{f}_{{n}} \left({x}\right)=\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\:\frac{{x}^{{k}} }{{k}!}\:. \\ $$

Question Number 30559    Answers: 0   Comments: 0

find I_n = ∫_0 ^1 (1−t^2 )^n dt .

$${find}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\left(\mathrm{1}−{t}^{\mathrm{2}} \right)^{{n}} {dt}\:\:. \\ $$

Question Number 30558    Answers: 0   Comments: 0

find I= ∫_(1/2) ^1 arctan((√(1−x^2 )) dx .

$${find}\:{I}=\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:{arctan}\left(\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:\:\:{dx}\:\:.\right. \\ $$

Question Number 30557    Answers: 0   Comments: 0

if ϕ convexe and f continue on [a,b] prove that ϕ( (1/(b−a)) ∫_a ^b f(t)dt)≤ (1/(b−a)) ∫_a ^b ϕof(t)dt.

$${if}\:\varphi\:{convexe}\:{and}\:{f}\:{continue}\:{on}\:\left[{a},{b}\right]\:{prove}\:{that} \\ $$$$\varphi\left(\:\frac{\mathrm{1}}{{b}−{a}}\:\int_{{a}} ^{{b}} \:{f}\left({t}\right){dt}\right)\leqslant\:\frac{\mathrm{1}}{{b}−{a}}\:\int_{{a}} ^{{b}} \:\varphi{of}\left({t}\right){dt}. \\ $$

Question Number 30556    Answers: 0   Comments: 0

let S_n (x)= Σ_(k=1) ^n ((sin(kx))/(k^2 (k+1))) find lim_(n→∞) S_n (x).

$${let}\:\:{S}_{{n}} \left({x}\right)=\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\:\frac{{sin}\left({kx}\right)}{{k}^{\mathrm{2}} \left({k}+\mathrm{1}\right)}\:\:{find}\:{lim}_{{n}\rightarrow\infty} {S}_{{n}} \left({x}\right). \\ $$

Question Number 30555    Answers: 0   Comments: 0

find ∫_0 ^1 (dt/(√(1−t^4 ))) .

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\sqrt{\mathrm{1}−{t}^{\mathrm{4}} }}\:. \\ $$

Question Number 30554    Answers: 0   Comments: 0

find ∫_0 ^∞ ((xcosθ +1)/(x^2 +2xcosθ +1))dx .

$${find}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{xcos}\theta\:+\mathrm{1}}{{x}^{\mathrm{2}} \:+\mathrm{2}{xcos}\theta\:+\mathrm{1}}{dx}\:. \\ $$

Question Number 30553    Answers: 0   Comments: 3

find lim_(x→0) (1+sinx)^x −(1+x)^(sinx) .

$${find}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \left(\mathrm{1}+{sinx}\right)^{{x}} \:−\left(\mathrm{1}+{x}\right)^{{sinx}} . \\ $$

  Pg 1758      Pg 1759      Pg 1760      Pg 1761      Pg 1762      Pg 1763      Pg 1764      Pg 1765      Pg 1766      Pg 1767   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com