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Question Number 145756 Answers: 2 Comments: 0

Question Number 145809 Answers: 1 Comments: 0

prove 1+2+3+.....=−(1/(12))

$$\mathrm{prove}\:\mathrm{1}+\mathrm{2}+\mathrm{3}+.....=−\frac{\mathrm{1}}{\mathrm{12}} \\ $$

Question Number 145751 Answers: 1 Comments: 4

Question Number 145750 Answers: 0 Comments: 0

find Σ_(n=0) ^∞ (((−1)^n )/((2n+1)^3 (n+3)^2 ))

$$\mathrm{find}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{3}} \left(\mathrm{n}+\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 145749 Answers: 1 Comments: 0

g(x)=log(tan(x)) developp g at fourier serie

$$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{log}\left(\mathrm{tan}\left(\mathrm{x}\right)\right)\:\mathrm{developp}\:\mathrm{g}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 145748 Answers: 1 Comments: 0

f(x)=arctan(2sinx) developp f at fourier serie

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{arctan}\left(\mathrm{2sinx}\right) \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 145763 Answers: 1 Comments: 0

if z=(((3+i sin θ)/(4−i cos θ)))is purely real and (Π/2)<θ<Π then find arg(sin θ +i cos θ)?

$${if}\:{z}=\left(\frac{\mathrm{3}+{i}\:\mathrm{sin}\:\theta}{\mathrm{4}−{i}\:\mathrm{cos}\:\theta}\right){is}\:{purely}\:{real}\:{and}\: \\ $$$$\frac{\Pi}{\mathrm{2}}<\theta<\Pi\:{then}\:{find}\:{arg}\left(\mathrm{sin}\:\theta\:+{i}\:\mathrm{cos}\:\theta\right)? \\ $$

Question Number 145746 Answers: 0 Comments: 0

find ∫_0 ^1 log(x)log(1−x)log(1−x^2 )dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{log}\left(\mathrm{x}\right)\mathrm{log}\left(\mathrm{1}−\mathrm{x}\right)\mathrm{log}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$

Question Number 145745 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((cos(2x))/((x^2 +1)^2 (x^2 +4)))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}\right)}\mathrm{dx} \\ $$

Question Number 145755 Answers: 0 Comments: 0

Let a,b,c > 0 and abc = 1. Prove that ((8(a^2 +1)(b^2 +1)(c^2 +1))/((a+1)(b+1)(c+1))) ≤ (a+b)(b+c)(c+a)

$$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:{abc}\:=\:\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that}\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{8}\left({a}^{\mathrm{2}} +\mathrm{1}\right)\left({b}^{\mathrm{2}} +\mathrm{1}\right)\left({c}^{\mathrm{2}} +\mathrm{1}\right)}{\left({a}+\mathrm{1}\right)\left({b}+\mathrm{1}\right)\left({c}+\mathrm{1}\right)}\:\leqslant\:\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right) \\ $$

Question Number 145729 Answers: 0 Comments: 0

Dl of f(x)=(√(x(1+x)))e^(3/(2x)) ..

$$\mathrm{Dl}\:\:\:\mathrm{of}\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}\left(\mathrm{1}+\mathrm{x}\right)}\mathrm{e}^{\frac{\mathrm{3}}{\mathrm{2x}}} .. \\ $$

Question Number 145724 Answers: 5 Comments: 1

Question Number 145723 Answers: 1 Comments: 0

Question Number 145722 Answers: 0 Comments: 0

Question Number 145721 Answers: 0 Comments: 0

if a;b∈N ; a≠b and a+b=2x find (a∙b)_(max) =?

$${if}\:\:{a};{b}\in\mathbb{N}\:\:;\:\:{a}\neq{b}\:\:{and}\:\:{a}+{b}=\mathrm{2}{x} \\ $$$${find}\:\:\left({a}\centerdot{b}\right)_{\boldsymbol{{m}}{ax}} =? \\ $$

Question Number 145718 Answers: 0 Comments: 1

F_1 = 3 N ; F_2 = 4 N ; F_3 = 6 N F_(max) - F_(min) = ?

$${F}_{\mathrm{1}} \:=\:\mathrm{3}\:{N}\:\:;\:\:{F}_{\mathrm{2}} \:=\:\mathrm{4}\:{N}\:\:;\:{F}_{\mathrm{3}} \:=\:\mathrm{6}\:{N} \\ $$$${F}_{\boldsymbol{{max}}} \:\:-\:\:{F}_{\boldsymbol{{min}}} =\:? \\ $$

Question Number 145716 Answers: 0 Comments: 0

can we use the pearson′s correlation and chi−square test for hypothesis interchangably? both test is used to find significant relationship between two variables.

$${can}\:{we}\:{use}\:{the}\:{pearson}'{s}\:{correlation}\:{and}\:{chi}−{square} \\ $$$${test}\:{for}\:{hypothesis}\:{interchangably}? \\ $$$${both}\:{test}\:{is}\:{used}\:{to}\:{find}\:{significant}\:{relationship} \\ $$$${between}\:{two}\:{variables}. \\ $$

Question Number 145715 Answers: 4 Comments: 1

Question Number 146130 Answers: 0 Comments: 0

(2^k +1)(3^k +2)≡0(mod k+5) min k=? (k∈N)

$$\:\:\left(\mathrm{2}^{\mathrm{k}} +\mathrm{1}\right)\left(\mathrm{3}^{\mathrm{k}} +\mathrm{2}\right)\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{k}+\mathrm{5}\right) \\ $$$$\:\mathrm{min}\:\mathrm{k}=?\:\:\:\left(\mathrm{k}\in\mathbb{N}\right) \\ $$

Question Number 145701 Answers: 2 Comments: 1

Question Number 145687 Answers: 0 Comments: 0

if q≥3 ; a>-1 then: (1+a)^q ≥ (1+2a)(1+a)^(q-2) ≥ 1+qa

$${if}\:\:{q}\geqslant\mathrm{3}\:;\:{a}>-\mathrm{1}\:\:{then}: \\ $$$$\left(\mathrm{1}+{a}\right)^{\boldsymbol{{q}}} \:\geqslant\:\left(\mathrm{1}+\mathrm{2}{a}\right)\left(\mathrm{1}+{a}\right)^{\boldsymbol{{q}}-\mathrm{2}} \:\geqslant\:\mathrm{1}+{qa} \\ $$

Question Number 145683 Answers: 1 Comments: 0

((3 ((360))^(1/(√4)) −2 ((162))^(1/(!3)) )/( (√(10))−(√2))) =?

$$\:\frac{\mathrm{3}\:\sqrt[{\sqrt{\mathrm{4}}}]{\mathrm{360}}\:−\mathrm{2}\:\sqrt[{!\mathrm{3}}]{\mathrm{162}}}{\:\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}}\:=? \\ $$

Question Number 145678 Answers: 0 Comments: 0

let X_1 and X_(2 ) be independent random variable of uniform distribution . If it is known that X_i ∼uniform (0,1) and let S = X_1 + X_2 Determine the Probability density function from S!

$${let}\:{X}_{\mathrm{1}} \:{and}\:{X}_{\mathrm{2}\:} \:{be}\:{independent}\:{random}\:{variable}\: \\ $$$${of}\:{uniform}\:{distribution}\:.\:{If}\:{it}\:{is}\:{known}\:{that} \\ $$$${X}_{{i}} \sim{uniform}\:\left(\mathrm{0},\mathrm{1}\right)\:{and}\:{let}\:{S}\:=\:{X}_{\mathrm{1}} \:+\:{X}_{\mathrm{2}} \\ $$$${Determine}\:{the}\:{Probability}\:{density}\:{function} \\ $$$${from}\:{S}! \\ $$

Question Number 145676 Answers: 2 Comments: 0

... advanced ......calculus... prove that: Σ_(n=1) ^∞ (((−1)^(n−1) )/(n^( 3) ((( 2n)),(( n)) ))) = (2/5) ζ (3 )

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{advanced}\:......{calculus}... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{prove}\:{that}:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\:\mathrm{3}} \:\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:\:{n}}\end{pmatrix}}\:=\:\frac{\mathrm{2}}{\mathrm{5}}\:\zeta\:\left(\mathrm{3}\:\right) \\ $$$$ \\ $$

Question Number 145675 Answers: 3 Comments: 0

the probabilty density function is known as follows : f(x) = {_(0 , x other) ^(cx^3 , 0 < x < 4) define P(1 < x < 2)!

$${the}\:{probabilty}\:{density}\:{function} \\ $$$${is}\:{known}\:{as}\:{follows}\:: \\ $$$${f}\left({x}\right)\:=\:\left\{_{\mathrm{0}\:\:\:,\:{x}\:{other}} ^{{cx}^{\mathrm{3}} \:\:\:,\:\mathrm{0}\:<\:{x}\:<\:\mathrm{4}} \right. \\ $$$${define}\:{P}\left(\mathrm{1}\:<\:{x}\:<\:\mathrm{2}\right)! \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 145674 Answers: 0 Comments: 0

the probability density function with two continous random variable X and Y is a follows : f(x,y) = {_(0 , x other) ^(2x + 2y , 0 < x < 1, 0 < y < 1) determine the correlation coefficient between X and Y!

$${the}\:{probability}\:{density}\:{function}\:{with}\:{two}\:{continous}\:{random} \\ $$$${variable}\:{X}\:{and}\:{Y}\:{is}\:{a}\:{follows}\:: \\ $$$$ \\ $$$${f}\left({x},{y}\right)\:=\:\left\{_{\mathrm{0}\:\:,\:{x}\:{other}} ^{\mathrm{2}{x}\:+\:\mathrm{2}{y}\:\:,\:\mathrm{0}\:<\:{x}\:<\:\mathrm{1},\:\mathrm{0}\:<\:{y}\:<\:\mathrm{1}} \right. \\ $$$$ \\ $$$${determine}\:{the}\:{correlation}\:{coefficient} \\ $$$${between}\:{X}\:{and}\:{Y}! \\ $$

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