Find the area between the two curves 2 1+2x²¹ Sketch the region in question. y = y = 2x² - 1

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A: The slope of the cone is L

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Q: Evaluate (x+y-52) dV where E = {(x, y, z) | − 7≤ y ≤0,0≤x≤y, 0≤ z ≤ x + y²}

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Q: 2. Prove that if d is a metric for X, then another metric d' for X is given by if a ≤ b " if b ≤ a…

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Q: 8z Compute the inverse z-transforms of z²-6z+25

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Q: Let B = a = The function p(t) = 2 + 4(t − 5) + 7(t − 5)², can also be written as p(t) = a + b(t − 2)…

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Q: u v If (x + iy)³ = u + iv, then show that + = (x² - y²). - X y ---

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Q: 7. Let X be a topological space, let A C X be a subspace, and let i: A → X the inclusion map. Fix a…

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Q: Use the substitution to solve the symmetric equation [Hint: We have x² + 1 x6 − 8x5 + 7x² +32x³ +7x²…

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Q: The commutator [X, Y] of two matrices is defined by the equation [X, Y] = XY - YX. Two anticommuting…

A: Given, The commutator X,Y of two matrices is defined by the equation X,Y = XY-YX. A2 = I, B2 = I,…

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Q: The Fourier series of the function is given by f(x) -7x if 4 <x<0 if 0< I<, T f(x) ~co - Σen En cos…

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Q: {e-3t+ et cos 4t}

A: Evaluate Laplace transform:  Le-3t+etcos4t

Q: 3. Let X be a topological space and let f: X→ Sn a continuous map to the n-sphere. Prove the…

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Q: Use Stokes' Theorem to evaluate (integral) F (dot) dr. C is oriented counterclockwise as viewd from…

A: here we will use stokes theorem for any vector field F  ∫CF.dr=∫∫S curlF dS where C is a positively…

Q: 6. Given the differential equation y (4) - y" - 2y + 2y = xe* + x² cosx. (a) The associated…

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Q: Prove by mathematical induction that n²n+2 is a solution to the recurrence relation r = -1 +2(n − 1)…

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Q: 0 0 0 -2 -2 -1 and B = 2 2 1 finding an invertible matrix P satisfying A = P-¹ BP. p-1 = Show that A…

A: Given A=000-2-2-1221 and B=-9-601280-9-60. To find an invertible matrix P such that A=P-1BP. We know…

Q: Which of the following graphs have hamiltonian circuits? P 0 M OA DC R I Н L H H U G H H OB S X OD R…

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Q: Find a singular value decomposition A = PDQT, where A = 1888) D = 1 Enter the matrices P, D, and QT…

A: The given problem is to find the singular value decomposition of the given matrix A where A=PDQT.

Q: Using the data below, determine who won based on the following voting methods.   Number of voters…

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Q: Jo (x) = -—- f* T cos(xcos 0) do = 1 -=-65² JO cos(xsin 0) de

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Q: 01 02 = = Find the singular values 01 0₂ of A = 2 1 # 0 -2 -2 1

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Q: The figure below shows that 4 one-inch segments are needed to make a 1 × 1 square, 12 one-inch…

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Q: The function f(x) = (x + 6)³ — 2ex² has two roots between x = −7 and x = 11. - 1. Plot f(x), -7 < x…

A: As per the question we are given a function as : f(x) = (x+6)3 - 2ex² Which has two roots between x…

Q: (e) Find the solution to the differential equation dy dx In x csc y = 0.

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Q: Suppose three tests are administered to a random sample of college students. Let X₁,..., Xy be…

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Q: Evaluate the integral by integrating with respect to x, y, and z. x=+1 64 SSS 00 4x-y Z (7).* + dx…

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Q: Prove that for all integers n, n2-n+3 is odd. (Write a standalone self-contained proof using…

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Q: V5    Use the Laplace transform to solve:   y′′ − 2y′ + y = t2δ(t − 3)   y(0) = 0

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Q: Let X be a topological space and let CX be the cone on X. (a) Show that CX is contractible.

A: As per norms, we will be answering the first question. If you need an answer to others, then kindly…

Q: Evaluate - III, ³ 3xz dV where E = {(x, y, z) | 1 ≤ x ≤ 4, x ≤ y ≤ 2x, 0 ≤ z ≤ x + 3y}

A: The given problem is to evaluate the given triple integral over the given region E.

Q: 1 / (√ECOS (2√7) 1 √t cos(2√t)√t cosh² (√t), (i cosh² (√)) dt

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Q: If A, B, C, and D are sets with A B and C D, and if A and C are disjoint BUD. and B and D are…

A: Given proposition A≈B and C≈D By the bijection                                  f:A∪C → B∪DDefine…

Q: Determine the Laplace transform of signal x(t) = = = [1 +t+e=²¹c cos(4t- TU u(t)

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Q: 12. C-1 더 13. C-1 ~ sle-28 8-31 2s (82 + +1)² 14. Find C-1 1 s1 ( 8(s + 1) J without using partial…

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Q: Prove: bd (s) = 5 TR-S bd (s) is a closed set

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Q: Suppose that g is a function of two independent variables that has continuous partial derivatives,…

A: Note: Directional derivative of f(x,y) at P(a,b) in the direction of v→ is given by: Dv→f(P)=(∇f.v^…

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Q: Find the area of the surface generated by revolving the curve y = √√x, 1 ≤ x ≤ 4, about the x-axis.…

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