Let f f(x)dx = 8 and f(f(x))²dx = 9. Find the following integrals: So cf(z)dz = f(f(x))²dx − (f f(x)dx)² = fb+7 f(x-7)dx=

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Q: 1. Find the general solution of the differential equation 9 dy dx when (a) r(x) = 0; (b) r(x) = ex;…

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Q: 3. For each of the following, if a circle has the dimensions given, de circumference: a. 6 cm…

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Q: 1. Solve the congruence x² + 1 = 0 mod 13³.

A: According to the given data, find the solution:

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Q: Let A 1 2 −1 -2 3 -2 -1 1 1 Diagonalize A to find A100.

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Q: 10. Find the area of each of the following. Leave your answers in terms of . (a) 5 cm 3 cm 60° (b)…

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Q: Consider the heat equation Ut = AUxx, a €R>⁰, 00 with boundary conditions ux (0, t) = ux (L, t) = 0,…

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Q: (ii) Let W be the subspace of R4 which is spanned by the vectors a₁ = (-1, 1, 2,5), a₂ = (0,…

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Q: 56. The region bounded by the graph of f(x) = 3x² + 1 and the x-axis on the interval [-1, 1].

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Q: Suppose that 11 female and 9 male applicants have been successfully screened for 5 positions. If the…

A: Suppose that 11 female and 9 male applicants have been successfully screened for 5 positions. If the…

Q: 3y 8 4 6 1 2 t² - 11 7 10 [18+x 8 4 2 1 у у 7 101

A: We have to find  and .

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Q: Question 3 (a) Determine the partial derivatives of the following functions with respect to each of…

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Q: 9. Find the area of ze zy that lies inside the cylinder z² + y² = 1.

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Q: For the vector field (x³z², o, -x²z), evaluate the line integral on the clase curve made by a square…

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Q: 7. You have a system of three forces that are hanging from a beam. Determine the Cartesian…

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Q: Consider the heat equation Ut = auxx, a € R⁰, 00 with boundary conditions ur(0, t) = u(L,t) = 0, t>…

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Q: 2. Construct a metric space (X, d) and an open set UC X such that U is not the union of countably…

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Q: Use Green's Theorem to evaluate the line integral [(y-x) dx + (2x−y) dy for the given path. C:…

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Q: Let S = decimal places.) 10000100 x 1. Note that In(n+1) 5 S S 1 + In(n). Note that the sequence (a)…

A: We have to Approximate r using a100 (Round your answer to four decimal places)

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Q: 6. Show that the special orthogonal group is compact. SO(n) := {A = O(n)| det A = 1}

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Q: For each of the following functionals, find the Gâteaux differential and use it to derive the…

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Q: Use iteration to guess an explicit formula for the recursively defined sequence and make use of a…

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Q: If a is a similarity of ratio r and A, B, and C are distinct non-collinear points, let A' = a (A),…

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