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Question Number 98531 Answers: 0 Comments: 0

Question Number 98528 Answers: 0 Comments: 2

Question Number 98521 Answers: 1 Comments: 0

Question Number 98520 Answers: 1 Comments: 0

Integrate the function f(x,y) = xy(x^2 +y^2 ) over the domain R:{−3≤x^2 −y^2 ≤3, 1≤xy≤4}

$$\mathrm{Integrate}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{xy}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right) \\ $$$$\mathrm{over}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{R}:\left\{−\mathrm{3}\leqslant\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \leqslant\mathrm{3},\:\mathrm{1}\leqslant\mathrm{xy}\leqslant\mathrm{4}\right\} \\ $$

Question Number 98516 Answers: 2 Comments: 2

Question Number 98506 Answers: 0 Comments: 1

Question Number 98470 Answers: 0 Comments: 0

prove that asymtotes y=mx−((∂xφ_K )/φ_n ) k=n−1 cuts the curve Σ_(r=0) ^n φ_r ((y/x))x^r in n(n−1) points

$${prove}\:{that}\:{asymtotes}\: \\ $$$${y}={mx}−\frac{\partial{x}\phi_{{K}} }{\phi_{{n}} } \\ $$$${k}={n}−\mathrm{1} \\ $$$$ \\ $$$${cuts}\:{the}\:{curve}\: \\ $$$$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\phi_{{r}} \left(\frac{{y}}{{x}}\right){x}^{{r}} \\ $$$${in}\:{n}\left({n}−\mathrm{1}\right)\:{points} \\ $$$$ \\ $$

Question Number 98468 Answers: 2 Comments: 10

Question Number 98464 Answers: 1 Comments: 0

Working individually, A, B and C can finish a piece of work in 16 days, 20 days and 30 days respectively. In how many days can A, B and C together complete a work which is 3(1/2) times the previous work?

$$\mathrm{Working}\:\mathrm{individually},\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{can} \\ $$$$\mathrm{finish}\:\mathrm{a}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{work}\:\mathrm{in}\:\mathrm{16}\:\mathrm{days},\:\mathrm{20}\:\mathrm{days} \\ $$$$\mathrm{and}\:\mathrm{30}\:\mathrm{days}\:\mathrm{respectively}.\:\mathrm{In}\:\mathrm{how}\:\mathrm{many} \\ $$$$\mathrm{days}\:\mathrm{can}\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{together}\:\mathrm{complete} \\ $$$$\mathrm{a}\:\mathrm{work}\:\mathrm{which}\:\mathrm{is}\:\mathrm{3}\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{times}\:\mathrm{the}\:\mathrm{previous} \\ $$$$\mathrm{work}? \\ $$

Question Number 98463 Answers: 1 Comments: 0

Question Number 98461 Answers: 3 Comments: 1

Question Number 98453 Answers: 0 Comments: 2

(m/(1×2))×(m/(2×3))×(m/(3×4))×...×(m/(99×100))=99 m?

$$\frac{{m}}{\mathrm{1}×\mathrm{2}}×\frac{{m}}{\mathrm{2}×\mathrm{3}}×\frac{{m}}{\mathrm{3}×\mathrm{4}}×...×\frac{{m}}{\mathrm{99}×\mathrm{100}}=\mathrm{99} \\ $$$$ \\ $$$${m}? \\ $$

Question Number 98613 Answers: 0 Comments: 0

Question Number 98450 Answers: 0 Comments: 1

Find the supremum and the infimum of f(x) = (x/(sin x)) ,x∈ (0,(π/2) ]

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{supremum}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{infimum}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}}{\mathrm{sin}\:\mathrm{x}}\:,\mathrm{x}\in\:\left(\mathrm{0},\frac{\pi}{\mathrm{2}}\:\right] \\ $$

Question Number 98448 Answers: 1 Comments: 5

6^(273) +8^(273) :49 prove the division

$$\:\:\:\:\:\:\:\mathrm{6}^{\mathrm{273}} +\mathrm{8}^{\mathrm{273}} \:\::\mathrm{49}\:\:\:\boldsymbol{{prove}}\:\:\boldsymbol{{the}}\:\:\boldsymbol{{divi}\mathrm{s}{ion}} \\ $$

Question Number 98445 Answers: 2 Comments: 0

give at form of serie U_n =∫_0 ^1 ((x^n ln(x))/((1+x)^2 ))dx

$$\mathrm{give}\:\mathrm{at}\:\mathrm{form}\:\mathrm{of}\:\mathrm{serie}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{x}^{\mathrm{n}} \mathrm{ln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 98444 Answers: 1 Comments: 0

calculate ∫_0 ^1 ((lnx)/((1+x)^2 ))dx

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

Question Number 98443 Answers: 1 Comments: 0

Given the sequence (U_n )_(n∈N) defined by U_0 =1 and U_(n+1) =f(U_n ) where f(x)=(x/((x+1)^2 )) Show by mathematical induction that ∀n∈N^∗ 0<U_n ≤(1/n)

$$\mathcal{G}\mathrm{iven}\:\mathrm{the}\:\mathrm{sequence}\:\left(\mathrm{U}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{defined}\:\mathrm{by}\:\mathrm{U}_{\mathrm{0}} =\mathrm{1}\:\mathrm{and} \\ $$$$\mathrm{U}_{\mathrm{n}+\mathrm{1}} =\mathrm{f}\left(\mathrm{U}_{\mathrm{n}} \right)\:\mathrm{where}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{x}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\: \\ $$$$\mathcal{S}\mathrm{how}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{that}\:\forall\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\mathrm{0}<\mathrm{U}_{\mathrm{n}} \leqslant\frac{\mathrm{1}}{\mathrm{n}} \\ $$

Question Number 98434 Answers: 0 Comments: 5

prove that Ω=Σ_(n=0) ^(+∞) Σ_(m=0 ) ^(+∞) ((Γ(n+(1/2)).Γ(m+(1/2)))/(Γ(n+1).Γ(m+1))).((((2/3))^n .((1/2))^m )/((n+m+(1/2)))) =((√3)/(2(√2))).G_(2,2) ^(2,2) ((1/4)∣_(0 , 0) ^((1/2),(1/2)) ) =(((√3)π)/(√2))K((3/4))=(((√3)π^2 )/(2(√2)AGM(1,(1/2))))

Question Number 98430 Answers: 1 Comments: 0

let g(x) =(2/(cos(πx))) developp g at fourier serie

$$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{2}}{\mathrm{cos}\left(\pi\mathrm{x}\right)}\:\:\mathrm{developp}\:\mathrm{g}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 98429 Answers: 1 Comments: 0

let f(x) =cos(αx) developp f at fourier serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{cos}\left(\alpha\mathrm{x}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 98416 Answers: 3 Comments: 0