Let f (x, y, z) = -12x? – y + 5z?. Calculate Vf (0, 5, 6). %3D (Write your solution using the form (*,*,*). Use symbolic notation and fractions where needed.) Vf (0,5, 6) =

Q: Question 7. Prove or disprove: (a) The union of two subgroups of a group (G, *) is a subgroup of G.…

A: 7)  We need to prove or disprove the given statements. a) The union of two subgroups of a group G ,…

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A: Alternating group is the group of even permutations. Detailed solution typesetted in the next step.

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A: This is a problem of complex analysis.

Q: 7 dx x2 + 4x + 8 00

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A: Nullity of A and Col(A)

Q: See attached image. Please provide a solution with a detailed explanation of steps.

A:

Q: Find the Fourier sine and cosine transform of f (x), if х, 0 2

A: Fourier Cosine transform and Fourier sine transform

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A: The plane surface is open.

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Q: 5 + y% b) lim (1,y)→(0,0) xª +y4

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Q: 3. Evaluate (2ry - )+(r +2:)7+(2y- 2r2)k) - dr, where C is a simple curve from (-3,-2,-1) to (1, 2,…

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Q: r(t) ti+ 8 sin(t)j + 8 cos(t)k u(t) + 8 sin(t)j + 8 cos(t)k (a) r'(t) = (b) r"(t) = (c) D[r(t) ·…

A: Note: We are allowed to solve three subparts at a time so upload remaining parts as next question.

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A: Here we use divergence theorem .

Q: luate the triple integral /// V² + y² + z² dV over the spherical shell E 9.

A: Integration using spherical coordinates

Q: use the Laplace Transform Table to find the inverse transform i e 35 3²Cs²+4) F6S) =

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Q: Part 2. Prove that the following are equivalent A. by Constructing a truth table 1. [p V (~ p ^q] →…

A: A) prove that the following are equivalent by constructing truth table 1) p∨~p∧q↔p∧q 2)…

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A: Solution :-

Q: (b) Use Stoke's Theorem to evaluate the line integral $ (3? – 22) dr + (z² – x²) dy + (y² – x²) dz,…

A: Stokes theorem  ∮CF.dr=∫∫SCurl F .dS Where S be a smooth surface that is bounded by a  closed,…

Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: Question 8. Define a relation - on the set of rational numbers Q by a ~ b iff Ja| = |b| (a) Prove…

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Q: Let f, g: R → R defined by if x 1 f(x) = %3D and g(x) = 3x + 2. %3D fog and go f.

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Q: What is the iterative method in system of linear equations? 2. Give atleast two examples of each…

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Q: For the following matrix 3 2 A = 3 7 -2 -3 2 8 10 20 || -10. Find approximate value for the…

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Q: b) Consider the following LP problem. Maximize z = 3x1 + 4x2 + X3 Subject to X1 + x2 + x, 5 50 2x, –…

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Q: EXAMPLE 3 Evaluate fE Vx + z'dv, where E is the region bounded by the paraboloid y = x + z and the…

A: To evaluate the below triple integral. ∫∫∫Ex2+z2dV Here E is the region bounded by the paraboloid…

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A: This is a problem of differential geometry.

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Q: R.3. Let [a, b] be an interval on the real number line (with a < b). Prove that a,b]-[0,1].

A: We have to find a continuous bijective from a,b to 0,1 to show that a,b~0,1

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A: Given,x2y"-xy'+y=ln(x) , y(1)=0 , y(2)=-5, n=8To find: Solution of given Boundary value problem

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A: Given  A~B and B~C we have to show that A~C.

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Q: 2. (D² – 4)y = 0 when y(0) = 0, y' = 3 %3D

A: To solve the given differential equation.

Q: 19. Solve y'(1) + y(t) = sin t; y(0) = 1 by Laplace transfrom. %3D

A: