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Question Number 41051 Answers: 0 Comments: 1

find the value of Σ_(n=1) ^∞ ((2n+3)/(n^2 (n+1)^2 ))

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{2}{n}+\mathrm{3}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 41049 Answers: 0 Comments: 2

calculate ∫_(−(π/4)) ^(π/4) (x^2 /(cos^2 x))dx

$${calculate}\:\:\:\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{x}^{\mathrm{2}} }{{cos}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 41044 Answers: 1 Comments: 0

Question Number 41038 Answers: 1 Comments: 5

Question Number 41032 Answers: 1 Comments: 0

(a/(x−a)) +(b/(x−b))=2.find x.

$$\frac{{a}}{{x}−{a}}\:+\frac{{b}}{{x}−{b}}=\mathrm{2}.{find}\:{x}. \\ $$

Question Number 41027 Answers: 1 Comments: 0

Question Number 41026 Answers: 1 Comments: 0

Question Number 41023 Answers: 0 Comments: 1

Question Number 47179 Answers: 1 Comments: 0

Question Number 47182 Answers: 0 Comments: 3

calculate ∫_0 ^1 e^(−x) (√(1−(√x)))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{x}} \sqrt{\mathrm{1}−\sqrt{{x}}}{dx}\: \\ $$

Question Number 41016 Answers: 1 Comments: 1

Question Number 41028 Answers: 1 Comments: 0

if 1/u = (√((x2 + y2 +z2))) then x∂u/∂x + y∂u/∂y + z∂u/∂z = ?

$${if}\:\mathrm{1}/{u}\:=\:\sqrt{\left({x}\mathrm{2}\:+\:{y}\mathrm{2}\:+{z}\mathrm{2}\right)} \\ $$$${then}\:{x}\partial{u}/\partial{x}\:+\:{y}\partial{u}/\partial{y}\:+\:{z}\partial{u}/\partial{z}\:=\:? \\ $$

Question Number 41009 Answers: 1 Comments: 1

Question Number 41003 Answers: 2 Comments: 0

The LCM and GCF of x,18 and 60 are 360 and 6 respectively. find the value of x

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{LCM}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{GCF}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{x}},\mathrm{18}\:\boldsymbol{\mathrm{and}}\:\mathrm{60} \\ $$$$\boldsymbol{\mathrm{are}}\:\mathrm{360}\:\boldsymbol{\mathrm{and}}\:\mathrm{6}\:\boldsymbol{\mathrm{respectively}}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{x}} \\ $$

Question Number 40984 Answers: 0 Comments: 1

let f(x) =∫_0 ^∞ te^(−t^2 ) arctan(xt)dt 1) find a simple form of f(x) 2) calculate ∫_0 ^∞ te^(−t^2 ) arctantdt and ∫_0 ^∞ t e^(−t^2 ) arctan(2t)dt 3)let u_n =∫_0 ^∞ t e^(−t^2 ) arctan(nt)dt find lim_(n→+∞) u_n study the convergence of Σ u_n

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:{te}^{−{t}^{\mathrm{2}} } \:{arctan}\left({xt}\right){dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:{te}^{−{t}^{\mathrm{2}} } {arctantdt}\:{and} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:{t}\:{e}^{−{t}^{\mathrm{2}} } \:{arctan}\left(\mathrm{2}{t}\right){dt} \\ $$$$\left.\mathrm{3}\right){let}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:{t}\:{e}^{−{t}^{\mathrm{2}} } {arctan}\left({nt}\right){dt} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {u}_{{n}} \\ $$$${study}\:{the}\:{convergence}\:{of}\:\Sigma\:{u}_{{n}} \\ $$

Question Number 40975 Answers: 2 Comments: 0

Question Number 40974 Answers: 0 Comments: 0

X = (x_1 , x_2 , ..., x_n ), X∈P^n Does there exist a point in N-dimensions, such that the points and line length (from origin) are prime? That is, Σ_(i=1) ^n x_i ^2 =p^2 , p∈P

$${X}\:=\:\left({x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:...,\:{x}_{{n}} \right),\:\:\:\:{X}\in\mathbb{P}^{{n}} \\ $$$$\: \\ $$$$\mathrm{Does}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{a}\:\mathrm{point}\:\mathrm{in}\:\mathrm{N}-\mathrm{dimensions}, \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{points}\:\mathrm{and}\:\mathrm{line}\:\mathrm{length}\:\left(\mathrm{from}\:\mathrm{origin}\right) \\ $$$$\mathrm{are}\:\mathrm{prime}? \\ $$$$\: \\ $$$$\mathrm{That}\:\mathrm{is}, \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{x}_{{i}} ^{\mathrm{2}} ={p}^{\mathrm{2}} ,\:\:\:{p}\in\mathbb{P} \\ $$

Question Number 40965 Answers: 1 Comments: 0