Show the 3-dimensional ball B₁: ((..) ER³ | x² + y² +2² <1²) is a Jordan set and Vol (B₁)= Vol (B₁). r> 0.

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Q: Lemma 10 Let FCK be a field extension. Let S and T be subsets of K Thon (SUT) - (T) where F₁ = F(S).

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Q: The gamma function, which plays an important role in advanced applications, is defined for n 21 by…

A: Given, The gamma function for n≥1 by   Γ(n) = ∫0∞ tn-1 e-t dt.

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Q: Consider the series 111 (8x)" n Find the interval of convergence of this power series by first using…

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Q: |x₁ + 2x₂ + 3x₂ =¬ Solve the linear equation systems 2x, +5x₂+2x, = -8 by using Crout method, where…

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Q: Kinematic viscosity of water (8) is related to temperature "T" in the following number: T D 40 1.66…

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Q: Let λ ER and consider the matrix J = 1 0 X 0 0 00 1 0 0 λ 1 0 0 X € M4. (a) Show that A is the only…

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Q: COS b) MTX -L The functions sin orthogonal set on -L≤x≤L, then show (MIX) cos (nIX) L COS L for m=…

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Q: 3. Determine half range Fourier sine series for f(x)=e^x in 0<x<m

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Q: 5. Consider the following linear programming problem: Minimize: C = 4x₁ + 5x2 subject to: 2x1 + x₂ ≥…

A: Given information Linear programming problem:- Minimize:  C=4x1 +5x2subject to:    2x1+x2 ≥12  x1+x2…

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Q: 3. O Find the best values of a, and a, if the line y=ax+a, is fitted to the d (0,-1), (2,5), (5,12),…

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Q: Let G = S4 and N {e, (1, 2) (3, 4), (1, 3) (2, 4), (1, 4) (2,3)}. Show that N is a normal subgroup.…

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Q: 21.5 Integrate the following function both analytically and using Simpson's rules, with n = 4 and 5.…

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Q: Let 7 = (1,0) and 7 = (0,1). The linear transformation T in R² transforms 27 + 37 to 37 +27 and 47…

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Q: y' = y²(1 + 2x), y(−1) = 1, dx = 0.5

A: Given: It is given that y'=y21+2x. Also, y-1=1 and dx=0.5 .

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Q: Consider many measurements with mean (x̄)and median (m), both of which are equal to 7. Which of the…

A: Consider many measurements with mean (x̄)and median (m), both of which are equal to 7. Which of the…

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Q: Problem 1: Diagonalize A and compute SAS-¹ to prove this formula for Ak: A 1 - [54] has Ak A² = [*…

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Q: Find four numbers in G.P. whose sum is 85 and product is 4096.

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Q: 1) The dimension of the subspace of P3 consisting of all vectors of the form at³+bt2 + ct+d, where b…

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Q: Determine a series solution to the initial-value problem (1+2x2)y′′+7xy′+2y =0, y(0)=0, y′(0)=1.

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Q: Consider the following. B = {(-2, 12, -9), (-1, 4, -3), (-3, 12, -8)), B' = {(3, 2, 4), (1, 1, 2),…

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Q: дz дz = z² əx ду 13. Solve completely the Lagrange PDE: x² +y² √ ² 02²2 =2 non-homogenous PDE (D³ –…

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Q: where A = Ife is defined ase=I+A+ *].0<x< , 0<x< 1 and I is identity matrix, then find the functions…

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Q: Question 1 [s variables Given the function of two f(x, y) = -4x² - 6xy-7y²-1. a) Use Lagrange…

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Q: Write the contrapositive of each statement.   If today is Sunday, then it is the weekend.…

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Q: If the temperature in a certain room is given by T(x, y, z) = x³ + 2y³ + 3z³ — xyz, what is the rate…

A: (a)  Given that the temperature of the room is                                           Tx,y,z =…