Use the divergence theorem F = tan−¹(5y + 8z)i + graphs of z = √√x² + y² to find the outward flux F.ndS of the vector field e²² + 5 cos xj + √√x² + y² + z² k, where S is the surface of the region bounded by the and x² + y² + z² = 49.

Q: Consider the shaded region in the graph below. Write SR f dA on this region as an iterated integral:…

A: (.)  Given iterated integral is,       where we will find the value of

Q: Follow the steps below to solve the given differential equation using series methods. Assuming the…

A: By using  , we will find the series solution of the given differential equation.

Q: Let v = (x²z, 2 –— 2xyz − 3y + x²y, 3z − x²z) be the velocity field of a fluid. Compute the flux of…

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Q: 3. Let T : R² → R² be defined by T = X Y -x+y x-y

A: 3. Given that  be defined by:

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Q: T T T F F F 11. 12. 13. If ab = 0 (mod 3), then a = 0 (mod 3) or b = 0 (mod 3). If ab = 0 (mod 6),…

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Q: 6. Let UC Rm be an open set. If h: U Rm is a homeomorphism and uniformly continuous on U, show that…

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Q: f(t) = ・ƒ(1) = f(t) (4 0 <1≤7 26 127 f(t) 0 ≤1<8 128 (1) = {cos[2(1-7 0 ≤t</ cos[2(1-7)] 12 an

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Q: (3) Let U = {(x, y, z) = R³ | x+y+z=0}. Let Pu : R³ → R³ be the linear transformation E given by…

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Q: Exercise 7. Let A = 1 2 3 0 1 2. Find the eigenvalues and eigenspaces of A. 3 7 11 Does R³ have a…

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Q: Each character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid…

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Q: Find the volume of the sphere in spherical coordinates with radius a by setting f-1 and evaluating V…

A: We have to find .

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Q: 2 (90) 2 Determine if S={ all the correct answers }is a basis for R2 and check a. S is a basis b.s…

A: Note: '' As per guidelines we will solve first question. If you want any specific question to be…

Q: 4. Show that is not equivalent to the usual metric space on R. 5. Is & topologically equivalent to…

A: Part 4 and 5 justified

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Q: 7.Use the graphs of f and g to evaluate the following 3 Ir t 3 . (a) (ƒ•g)(2) c) (fog)(1) d)…

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Q: Problem 2 . Let M(d) be the set of all matrices with the size d x d, where d E N and d≥ 2. (a)…

A: Given Information:The set is the collection of all matrices with the size .To show:a)  if  are…

Q: a) S SR y dA. Y b) S Sy dA

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Q: 1. Find the inverse of the following matrices by the [A[I] → [I|A¯¹] meth a. A A=|-7 -1⁰ 3 -1 -…

A: Here, we have to find the inverse of given matrices.

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Q: Find the volume of the solid obtained by rotating the region bounded by y = x, the line x = 4 and…

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Q: Suppose Q is the quadratic form below The minimum value of Q subject to = 1 is Q = 4. An eigenvector…

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Q: 1. Let B₁ = = {-1} {[]} i) Find Rep ii) Find Rep B1 and -{[]} B2 = be two ordered bases for R² C…

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Q: exponential functio

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Q: Consider the triangle below. Click on the picture to see it more clearly. In questions 1, 2 and 3…

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Q: Show that y₁ = ecos(2x) and y2 = e sin(2x) are two linearly independent solutions of d'y dy dz² +2-…

A: We have to show that  and  are two linearly independent solution of the differential equation

Q: The figure shows level curves of a function f(x, y). (a) Draw gradient vectors at P and Q. Is Vf(P)…

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Q: (e) Ray limited has three divisions which produce product A, B and C. The current survey, in 2021,…

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Q: Problem 1 Determine which of the following bases are orthogonal, and then determine which are…

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Q: 2. The equation that models the amount of time, +, in minutes that a cup of hot chocolate has been…

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Q: Evaluate the line integral feF. dr where F = (4 sin x, -3 cos y, 5xz) and C is the path given by…

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Q: Find the eigenvalues making sure that each 20 = Yn(x) = and eigenfunctions yn(x) for the given…

A: Here c1,c2 are arbitrary constants.

Q: Let V = R²×2 be the vector space of 2 × 2 matrices and let L : V → V be defined by L(X) = = image of…

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Q: Find the order of a modulo 7 for a = 1, 2, 3, 4, 5, 6.

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Q: 1. Let N be a Poisson process with intensity λ, with N = {N(t) : t ≥ 0} where N(t) denotes the…

A: The objective of this question is to prove that the interarrival times X1, X2,... in a Poisson…

Q: Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros…

A: First we find a root and then use division algorithm

Q: Let S be the surface shown in the following figure in the first octant in the xy-plane, and let 7 be…

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Q: a. Determine the position function for t≥ 0. s(t) =

A: (a) We know velocity = displacement/timeAlso displacement = velocity * time

Q: Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros…

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Q: X-2=2 2x+y=-7 5x+1-2x = ²5 rewrite in matrix form AX = b

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Q: Find the vectors T and N given the following vector function. r(t) = (sin³ t, cos³ t, sin² t)

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Q: 3. Find the volume of the solid generated when the area between the two curves is rotated about the…

A: Using cylindrical shell method:The radius of the cylindrical shell is AB=y+1The length of the…

Q: The general solution of the differential equation 2y""-3y"-2y'=0 corresponds to A- B- C- D- y=c₁e²…

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Q: Find an equation of the ellipse to the right. An equation of the ellipse is -105 DC 10 15 5- 10 Ay 5…

A: Given that:We have to find the equation of ellipse.