Solve the given initial-value problem. (x + 3) y(x) = dy dx + y = In(x), y(1) = 10 x(ln(x)-1) + 41 x + 3 Give the largest interval I over which the solution is defined. (Enter your answer using interval notation.) I = (0,∞) X

Q: Show that 38 = -1 (mod 17). Using this, deduce that 3 is a primitive root of 17.

A: We need to show that 38≡-1mod 17. Since 34=81≡-4mod 17 ⇒38=342≡-42mod 17

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A: Thr addition property of inequality-    For all number  a,b,c    If  a&gt;b then a+c &gt;b+c

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Q: Now we can do something similar with the two 2-point DFT's to get equations for a; for j = 0,1,2,3:…

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Q: Solve for the relative max value of g(x) = 45 17x²-3x³

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A: V=2π∫03x3x-x2dx   =2π∫033x2-x3dx   =2πx3-x4403   =2π27-814   =13.5π

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Q: (a) Directly use the Bolzano-Weierstrass theorem (Theorem 2.3.8) to prove that every Cauchy sequence…

A: Details attached in the next step.

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Q: Let : R² R² be given by f(x, y) = (x + 1, y + 1). f Let D₁ = {y}, D₂ = {x ≥y, x>0}. -

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Q: Does Sn have a subgroup isomorphic to An, other than An (n ≥ 5).

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Q: (see instructions for Exercise 6 in Section 2.2): PROOF EVALUATION a) "THEOREM": For any sets A, B,…

A: THEOREM: For any sets A, B, and C, if A∪B=A∪C, then B=C.