Given a real a > 0, compute the integral x² - a² sin(x) X 5.0⁰0 x² + a² -dx.

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Q: 2. Determine all distinct values of -i and plot these values in the complex plane.

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Q: A. Using the definition of limit, show that limn→∞ 1 / n5 = 0 and that limn→∞ 1 / n1/5 = 0.

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A: We can arrange these five sentences in 5! ways. Means 5! = 5x4x3x2x1 = 120.

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Q: solve the initial value problem y' + 2xy = x, y(0） = 2

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Q: Let (x) be a convergent sequence with lim (x) = x > 0. Prove that there exists an NE N such that -x…

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Q: 50 -c < x < 0 0 < x < C ƒ (x) = {0 C

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Q: 72 Σ2 = 2n+1. i=0 - 1

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Q: Suppose that G is a group of order 48. Show that the intersection ofany two distinct Sylow…

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Q: 8. Shade the sets с (with B B (Anc)n B and (ANC)UB.

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Q: Exercise III.2. Graph the following sets S in R² and determine which are conver: (i) B (ii) B:= • {…

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Q: How many Sylow 5-subgroups of S5 are there? Exhibit two.

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Q: Let's use Backward Secant Method Example 2. X¹ - 10000 start with x₁ = 2 and x2 = 3

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Q: (15) Let a, b = Z. Prove that if a is divisible by 4 and b is divisible by 4, then: (a) ab is…

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