Evaluating the integral 1 1 -dz, s(0,1) (z – a)(z – a¯!) prove that for any a E (0, 1), dt 1 + a? – 2a cos t 1- a²"

Q: 3 Evaluate the integral c Ħ A) 1 B) 77 c) - Ť tan?xdx E)ユ-

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Q: Use a Fourier sine expansion to solve ĉu ô’u ôt ôx? u(0,t) = u(1,1) =0,1> 0, = x sint in (0,1) ×…

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Q: Find the potential function f for the field F. F = (y - z) i + (x + 2y-z)j- (x+ y) k O f(x, y, z) =…

A: We have to find

Q: A. Demuestra que B={1+x,x+x,1+r} es una base para P2 espacio de polinomios de segundo grado). 2 B.…

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Q: Use the Laplace transform to solve th integral equation y() = 1- sinht - Jy()dr 5et le-!te | 4 4 OB.…

A: To solve the given integral equation first we will take the laplace transform of both side . We also…

Q: (a) Verify that the Fundamental Theorem for Line Integrals can be used to evaluate the integral Sc…

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Q: Given the Bessel identity 1 d a dr [æ" J„(ax)] = x' J,_1(ax), v > 0, a > 0, S a*J½(2æ)dx = 3 ,5 a)…

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Q: Evaluate the iterated integral S 4 0 rdz dr de (1-e²¹6) 6x{1+e+] 3x(1+e+) 7x (1-07) /(1-8-16)

A: To evaluate the iterated integral.

Q: Suppose that f(x, y, z) = (1+x + y² + z³)4 + ln (1 + 3x + 2y + z).

A: In this question, we approximate the function by using a linear approximation of f(x,y,z)

Q: 6) Evaluate the improper integrals ∞ 5 a) 5² (+ + e-") dx s (-x) е 2 7 5 b) ² = 8 dx 4x-8 2

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Q: Evaluate the integrals in Exercises 1–K. 1. [Pi + 7j + (t + 1)k] dt Го- 4 k dt 2. (6 – 6t)i + 3Vij +…

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