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Question Number 137597 Answers: 2 Comments: 0

Find the minimum value of x^(2) +y^(2) +z^(2) , subject to the condition 2x+3y+5z=30?

$$ \\ $$Find the minimum value of x^(2) +y^(2) +z^(2) , subject to the condition 2x+3y+5z=30?

Question Number 137594 Answers: 1 Comments: 0

(x+(√(x^2 +1)))(y+(√(y^4 +4)))=9 x(√(y^4 +4))+y(√(x^2 +1))=?

$$\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)\left({y}+\sqrt{{y}^{\mathrm{4}} +\mathrm{4}}\right)=\mathrm{9} \\ $$$${x}\sqrt{{y}^{\mathrm{4}} +\mathrm{4}}+{y}\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}=? \\ $$

Question Number 137592 Answers: 3 Comments: 0

......advanced.....calculus.... 𝛀=Σ_(n=1) ^∞ ((ψ′′(n))/n)=??? I havefound :: Ω=−(π^4 /(36)) ... !

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:......{advanced}.....{calculus}.... \\ $$$$\:\:\:\:\boldsymbol{\Omega}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\psi''\left({n}\right)}{{n}}=??? \\ $$$$\:{I}\:{havefound}\:::\:\:\Omega=−\frac{\pi^{\mathrm{4}} }{\mathrm{36}}\:\:...\:! \\ $$

Question Number 137591 Answers: 0 Comments: 1

a=(4)^(1/3) +(2)^(1/3) +(1)^(1/3) (3/a)+(3/a^2 )+(1/a^3 )=?

$${a}=\sqrt[{\mathrm{3}}]{\mathrm{4}}+\sqrt[{\mathrm{3}}]{\mathrm{2}}+\sqrt[{\mathrm{3}}]{\mathrm{1}} \\ $$$$\frac{\mathrm{3}}{{a}}+\frac{\mathrm{3}}{{a}^{\mathrm{2}} }+\frac{\mathrm{1}}{{a}^{\mathrm{3}} }=? \\ $$

Question Number 137590 Answers: 0 Comments: 1

x=1+((π+(π+1)^2 +(π+2)^3 +(π+3)^4 )/(4+5^2 +6^3 +7^4 )) (√(x+2(√(x−1))))+(√(x−2(√(x−1))))=?

$${x}=\mathrm{1}+\frac{\pi+\left(\pi+\mathrm{1}\right)^{\mathrm{2}} +\left(\pi+\mathrm{2}\right)^{\mathrm{3}} +\left(\pi+\mathrm{3}\right)^{\mathrm{4}} }{\mathrm{4}+\mathrm{5}^{\mathrm{2}} +\mathrm{6}^{\mathrm{3}} +\mathrm{7}^{\mathrm{4}} } \\ $$$$\sqrt{{x}+\mathrm{2}\sqrt{{x}−\mathrm{1}}}+\sqrt{{x}−\mathrm{2}\sqrt{{x}−\mathrm{1}}}=? \\ $$

Question Number 137588 Answers: 1 Comments: 0

For a positive number n , let f(n) be the value of f(n)=((4n+(√(4n^2 −1)))/( (√(2n+1)) +(√(2n−1)))) calculate f(1)+f(2)+f(3)+...+f(40).

$${For}\:{a}\:{positive}\:{number}\:{n}\:,\:{let} \\ $$$${f}\left({n}\right)\:{be}\:{the}\:{value}\:{of}\: \\ $$$${f}\left({n}\right)=\frac{\mathrm{4}{n}+\sqrt{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}}{\:\sqrt{\mathrm{2}{n}+\mathrm{1}}\:+\sqrt{\mathrm{2}{n}−\mathrm{1}}} \\ $$$${calculate}\:{f}\left(\mathrm{1}\right)+{f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+...+{f}\left(\mathrm{40}\right). \\ $$

Question Number 137585 Answers: 2 Comments: 0

Find the cube of the number N= (√(7(√(3(√(7(√(3(√(7(√(3(√(7(√(3...))))))))))))))))

$${Find}\:{the}\:{cube}\:{of}\:{the}\:{number}\: \\ $$$${N}=\:\sqrt{\mathrm{7}\sqrt{\mathrm{3}\sqrt{\mathrm{7}\sqrt{\mathrm{3}\sqrt{\mathrm{7}\sqrt{\mathrm{3}\sqrt{\mathrm{7}\sqrt{\mathrm{3}...}}}}}}}} \\ $$

Question Number 137584 Answers: 1 Comments: 0

Given { ((a_(2n) = a_n .a_2 +1)),((a_(2n+1) = a_n .a_2 −2 )) :} and { ((a_7 = 2)),((0<a_1 <1)) :}. Find a_(25) =?

$${Given}\:\begin{cases}{{a}_{\mathrm{2}{n}} \:=\:{a}_{{n}} .{a}_{\mathrm{2}} \:+\mathrm{1}}\\{{a}_{\mathrm{2}{n}+\mathrm{1}} \:=\:{a}_{{n}} .{a}_{\mathrm{2}} \:−\mathrm{2}\:}\end{cases}\:{and} \\ $$$$\:\begin{cases}{{a}_{\mathrm{7}} \:=\:\mathrm{2}}\\{\mathrm{0}<{a}_{\mathrm{1}} <\mathrm{1}}\end{cases}.\:{Find}\:{a}_{\mathrm{25}} \:=? \\ $$$$ \\ $$

Question Number 137582 Answers: 1 Comments: 0

A=(((1/3)((2)^(1/3) −1)((2)^(1/3) +1)^3 ))^(1/3)

$$\mathrm{A}=\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}}{\mathrm{3}}\left(\sqrt[{\mathrm{3}}]{\mathrm{2}}−\mathrm{1}\right)\left(\sqrt[{\mathrm{3}}]{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 137579 Answers: 1 Comments: 0

(−1)×(1/(π.i)) =?

$$\left(−\mathrm{1}\right)×\frac{\mathrm{1}}{\pi.{i}}\:=?\: \\ $$

Question Number 137575 Answers: 0 Comments: 0

Question Number 137574 Answers: 0 Comments: 0

Question Number 137568 Answers: 0 Comments: 2

Question Number 137563 Answers: 2 Comments: 0

let ((x^2 +y^2 )/(x^2 −y^2 ))+((x^2 −y^2 )/(x^2 +y^2 ))=k find the value of ((x^8 +y^8 )/(x^8 −y^8 ))+((x^8 −y^8 )/(x^8 +y^8 )) in terms of k

$${let}\:\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }+\frac{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }={k} \\ $$$${find}\:{the}\:{value}\:{of}\:\frac{{x}^{\mathrm{8}} +{y}^{\mathrm{8}} }{{x}^{\mathrm{8}} −{y}^{\mathrm{8}} }+\frac{{x}^{\mathrm{8}} −{y}^{\mathrm{8}} }{{x}^{\mathrm{8}} +{y}^{\mathrm{8}} } \\ $$$${in}\:{terms}\:{of}\:{k} \\ $$

Question Number 137559 Answers: 0 Comments: 2

What is the volume of tetrahedron ABCD, whose vertices have the coordinates A (2, 3, 6), B (3, 2, 2), C (3, 4, 7) and D (5, 1, 8). Find the lateral surface area of the tetrahedron and find the volume of the tetrahedron?

$$ \\ $$What is the volume of tetrahedron ABCD, whose vertices have the coordinates A (2, 3, 6), B (3, 2, 2), C (3, 4, 7) and D (5, 1, 8). Find the lateral surface area of the tetrahedron and find the volume of the tetrahedron?

Question Number 137558 Answers: 1 Comments: 0

(x+y)dx + (x+y^2 )dy = 0

$$\left({x}+{y}\right){dx}\:+\:\left({x}+{y}^{\mathrm{2}} \right){dy}\:=\:\mathrm{0}\: \\ $$

Question Number 137556 Answers: 0 Comments: 0

Question Number 137547 Answers: 0 Comments: 1

Question Number 137545 Answers: 0 Comments: 0

Question Number 137538 Answers: 0 Comments: 0

calculate ∫_(−∞) ^(+∞) ((2x+1)/((x^4 −2x^2 +3)^2 ))

$${calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{2}{x}+\mathrm{1}}{\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 137536 Answers: 1 Comments: 0

calculte ∫_(−∞) ^∞ ((sin(πx^2 ))/((x^2 +2x+2)^2 ))dx

$${calculte}\:\int_{−\infty} ^{\infty} \:\frac{{sin}\left(\pi{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 137535 Answers: 0 Comments: 0

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

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

Question Number 137530 Answers: 1 Comments: 0

If sin^(−1) (sin α+sin β)+sin^(−1) (sin α−sin β)=(π/2) find the value of sin^2 α+sin^2 β. [(1/2)]

$$\mathrm{If}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:\alpha+\mathrm{sin}\:\beta\right)+\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:\alpha−\mathrm{sin}\:\beta\right)=\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}^{\mathrm{2}} \alpha+\mathrm{sin}^{\mathrm{2}} \beta.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\frac{\mathrm{1}}{\mathrm{2}}\right] \\ $$

Question Number 137528 Answers: 3 Comments: 1

Question Number 137525 Answers: 0 Comments: 0

Question Number 137523 Answers: 1 Comments: 0

L=lim_(x→0) ((x!−1)/x)

$$\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}!−\mathrm{1}}{\mathrm{x}} \\ $$

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