Exercise 1 (Br(a) is closed). Recall that for a € R" and r > 0, we define Br(a) = B(a, r) := {x € R" : ||x — a|| ≤r}. Show that Br(a) is closed.

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Q: Z₁' (t) = -6₁2 + 1.12₁ -0.822 Z₂²' (t) = -13.8 +2.12, -1.222 Z₁ (0) =11 Z₂₁₂ (0) = 4

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Q: 3. (Section 17.6) Determine the upward flux of F = through the part of z = x2 + y2 below z = 2.

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Q: 3 -21 {0} -2 1 3 100 000

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Q: [X₁ + x₂ + x3 x4 3x1 +5x22x3 + x4 -3x₁7x₂+7x35x4 1+3x2 - 4x3 + 3x4 = 3 = 1 = 7 = -5.

A: The given system of equations

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Q: (10) Find all solutions of the congruence 2 = 22 (mod 53). C

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Q: (17) The graph of p(x) is shown below. What is the remainder when p(x) is divided by x+4? A) x-4

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Q: Compute the derivative ficts of the logistic sigmoid 1 foo. 1 + exp(-x)

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Q: The inverse Laplace transform of 28² +238-97 (s + 4) (s² 14s +85)' is: - peat + qeßt cos(wt) + reßt…

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Q: о усп) =X(=) 2) усл) =X(rn) з усп) =X(и-zn) Дусп) = x(n=-2n-1)

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Q: 10 Consider the function f(x) = 5x¹0 + 7x³ – 6x¹ – 4. Enter an antiderivative of f(x). Do not enter…

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