k=1 Functions f and G are defined by f(x) - sin x 1+x²¹ Find the derivative G'(0). G(x) = rx+π [*** f(x+t) dt, x € R.

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A: By using given definition of Laplace transform, we will find the Laplace of the given function.

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A: According to our guidelines we can solve only first three subparts.Kindly repost remaining subpart.

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A: The given function is  and the surface is bounded by the curves  and .Find  as follows.Put .So, the…

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Q: ) Find the outward flux of 7 = (x, y², z) through x² + y² + z² = 4.

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Q: Let F = (yey, xey) and let C be given by: x = sin(t), y et-¹ (1- = cos(πt)), 0≤ t ≤ 1. Show that is…

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Q: In Exercises 1-18, s = 1+2i, u = 3-2i, v = 4+i, w = 2-i, and z = 1+i. In each exercise, perform the…

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Q: Determine whether the following series converges. Justify your answer. 23 (3) Σ tan k=1

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Q: 2. Prove that the union of two disjoint sets, where one is countably infinite and the other is…

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Q: (a) Find the Fourier series of the function f(x) = x²,0 ≤ x < L with period L. In the following,…

A: Given function f(x)=x2 defined in [0,L] with period L.The Fourier series is of the…