Verify the Divergence Theorem for the vector field and region: (5x, 62, 8y) and the region x² + y² ≤ 1,0 ≤ z ≤ 9 = JsF-ds . = SSSR div(F) dV=

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A: Given: x1+2x2-x3=6x1-x2+2x3=-32x1-x2+x3=-1 To find: The values of x1, x2, x3 using Gauss-Seidel and…

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Q: Q14. A red and a blue die are thrown. Both dice are fair. The events A and B are defined as follows:…

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Q: evaluete the matrix of cofactors for Frix  (Ĉ) and det (A) emd A¹ -1 Ĉ, Č‚Ã', AM -

A: Introduction: By dividing the supplied matrix's adjugate by its determinant, the inverse matrix is…

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Q: Ibu Tami has an antique painting whose value increases following the following functions: V(t) =…

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Q: Consider the system 3x + 7y + 13z = 76 x + 5y + 3z = 28 12x + 3y - 5z = 1

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Q: 3 ={0.2) 14 The vectors B = 1 (2³) B = [ ²5 ] form a basis. Find a vector x given the B-coordinates…

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Q: 1- Use the method of Frobenius to obtain series solutions of the following. y" -xy' +y = 0.

A: Given a differential equation y''-xy'+y=0. Let y=∑n=0∞anxn be power series solution of given…

Q: (b) S= {[a b]]a,b ≤ R}, R = M₂ (R) Г. ורג n U

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Q: 7. The goal of this problem is a proof of the Lagrange form of the remainder in Taylor's theorem…

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Q: To show that the general factorial function: (a)m ere m is a positive integer and n is a non…

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Q: Two large containers A and 8 of the same size are filled with different fluids. The fluids in…

A: Answer  We get  t= 6.868192 Now step by step approach is as follows

Q: Statement 6.5. Let A be a finite set. If BC A, then B is finite.

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Q: a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the…

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Q: Differentiate implicitly to find d2y/dx2.   3y2−xy+5x2=5

A: Differentiate implicitly to find d2y/dx2.  3y^2−xy+5x^2=5

Q: If fixgy is continuous and X ₁3 path-connected, then so is f(x)

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Q: 8. Solve 2y"+y' = g(t); g(t) = (4t; t < 1, 16;t ≥ 1:y(0)=-6, y'(0)=1

A: Sol:- First write g(t) in terms of unit step function :- gt=4tt&lt;16t≥1gt=4t*Ht-Ht-1+6Ht-1Now , we…

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Q: For what interval is the graph of the rational function decreasing? 8 8 4 c) -0 4 -8 a) for no…

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Q: Find the general solution: y-9y'+14y=-4e³* +6sin 2x

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Q: Find ||A||₁ and ||A|| for the matrix A = 4 -1 -3 -3 2 0 5 6 1.

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Q: Let the matrix of L: R³ R² with respect to the bases S = and -{-}} W₁ T= c. Find L W2 O be A= a.…

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Q: Test the series for convergence or divergence. 8 WI n! 145"

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Q: Find y as a function of x if y(0) = 13, y' (0) = 22, y" (0) = 27. y(x) = y" - 15y" +56y' = 42e*,

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Q: Select all pairs in the reflexive closure of the relation R, defined on the set A = { a, b, c, d }…

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Q: Let f(x, y) = sin(xy) be a two variable function, and let y be an oriented path given by x = 2 cos…

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Q: 1. In each case explain why R is not a ring. (a) R= {0, 1,2,3,...}, operations of Z (b) R = 27 (c) R…

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Q: Definition of the logrithmic function: y = logb(x) if and only if by = x, where x > 0, b>0, b# 1.…

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Q: State only if standard form or not standard form.

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Q: 2. Evaluate the surface integral ff(x-2y+z)dS, S: z = 2, x² + y² ≤ 1. S

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Q: y"-9y' +14y=-4e³x + 6sin 2x

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Q: For the function f(x) = x² on the interval [0, 7], its full-odd periodic extention is ffo(x) = xx on…

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Q: Consider F and C below. F(x, y) = 8xy² i + 8x²y j C: r(t) = (t + sin(at), t t + cos(-1⁄nt)), (a)…

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Q: 5. Find the centroid of the region bounded by the curves: a) y = x³; x+y= 2; x = 0 b) y = x; and x =…

A: The area is bounded by y=x3; x+y=2; x=0 The point of intersection is 1,1, 0,0, 0,2…

Q: Let P(x) be the statement "x is happy" and Q(x) be the statement "x is under 20", where the universe…

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Q: Find the point on the graph of the given function at which the slope of the tange 2 f(x) = 8x² +…

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Q: 2. Let consider given points: (1,1), (3,2), (4,3), (5,6). (a) Find the best least square fit by a…

A: The least square method is the process of finding the best-fitting curve for a given data set. . The…

Q: Find A, B, AB, and [AB]. Then verify that |A||B| -2 1 1 ^-[¯² _²]- ® -[ 1 _²] A = 4 -2 -1 (a) |A|…

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Q: Show that the series (a > 0, ß > 0) a +1 (α+1) (2x + 1) (B+1) (2ß+1) + 1+ B+1 + (a + 1) (2x + 1) (3a…

A: We will use ratio test for convergence    To  check a series ∑anit is convergent or divergent first…

Q: 1- Use the method of Frobenius to obtain series solutions of the following. xy" +y¹-3y=0

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Q: 3. f(t) = 3e-2t+2

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Q: Click and drag the steps to determine whether the given pair of graphs are Isomorphic. 1451 1₂ 14…

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Q: Salmon swim up to 2000 miles upstream to spawn. Scientists have found that the oxygen consumption…

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Q: af Əx Recall that a differential equation of the form M(x, y) dx + N(x, y) dy = 0 is exact if there…

A: We have to write the differential equation in the form Mdx+Ndy=0, and have to find M, N.

Q: How many edges does a tree with 10,000 vertices have? Multiple Choice O 10,002 9998 10,001

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Q: The initial probability vector P and the transition matrix A are given for a three-state Markov…

A: Please check step 2 for solution!