Prove the following statements (a) Vn € N, (2i − 1)² = by mathematical induction: n(2n + 1)(2n − 1) . 3 i=1 (b) For all integers n ≥ 3, n² ≥ 2n + 1.

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Q: Prove the following statements (a) Vn € N, (2i − 1)² = n i=1 by mathematical induction: - n(2n +…

A: *By Bartleby policy I have to solve only first one as these are all unrelated  problems.These are…

Q: Permanente M 2 tf(x)=√x-1 et g(x) = x² +2. Le domaine et l'image de f Le domaine et l'image de g Les…

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Q: Find the general solution of the differential equation π y" + 4y = 13 sec² (2t), 0 < t < 4 NOTE: Use…

A: y''+4y=13sec22t, 0&lt;t&lt;π4 Auxiliary Equation r2+4=0⇒r=±-4⇒r=±2i hence complementary function…

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Q: 6. Evaluate the following real integrals by residue theorem 3 • I= 88 1527 dx (x²+1)(x² +9) ans 12

A: 6. To Evaluate: I=∫-∞∞dxx2+1x2+9

Q: How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 + x6 = 25 in which each xi is a…

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Q: 24. Solve the following integral using substitution method: f8x√2x² - 1dx

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Q: 3. Approximate the first order derivative of f(x)= x² + 2x at x = 3, using Forward, Backward and…

A: Formulas for differences are enclosed next page

Q: 13. If m (0,p) is the middle point between A (-2,-10) and B (q, 10). Calculate the value of p and q.

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Q: Consider the following system of linear equations, 2x1 + X1 3x1 -2x1 X2 + 2x₂ - - - - 3x3 + X4 2x3 +…

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Q: Example 22 Matrix B shows the number of sightings of rare birds made by members of a birdwatching…

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Q: Name the function of the graph below: -T/5 -4- 3- 2 0 --1- --2- --3- -4 f(t) = 3 cos (5πt) f(t) = 5…

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Q: Given differential equation y""-sy" -4y' + 8y = e²-³x, (D³ - 20² - Auxilary equation 4D +8)y=e +8x9…

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