Begin with the Maclaurin (Taylor) series: 7² 2¹ 2-6 cos x = 1 2! 4! 6! (a) Evaluate cos (). (b) List the zeros of cos r. (c) Expand cos z as an infinite product in the form where a, b, c, ... are the zeros of cosa. 1 + P(z)-(1-) (1-) (1-5)---

Q: .2п 0 cos² t 2 COS 13 + 12 cost dt

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A: we need to evaluate the triple integration. For finding the solution first we will find the limits…

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Q: 10. Using Cauchy's Residue Theorem, evaluate -2π (cos 30)² 1-2p cos 20+p² d0,0 < p < 1.

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Q: 1 If z = cos(0) + isin (0), prove that z³ + || COS (30)

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Q: 27 de Evaluate the intergal using the residue theorem. 12 + 6 sin e

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Q: (3) Prove that πόληΣ one (= -10+1}], [cos² (π (n 1)! π(κ) = n 25η Σα where “π” within the sum stands…

A: To show that the two quantities are equal it is enought to show that the function on the RHS takes…

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Q: röve the following identity () - (":")- (:-) n n n | k k k 1

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A: The residue of a function: f(z) at z=a is defined as Resz=af(z)=limz→az-af(z).

Q: (a) Evaluate . z²e1/z where c is z = 1.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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A: the sum of cube of first n terms I given by,

Q: de Evaluate the intergal using the residue theorem. 13 +4 sin e

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Q: 7 (4) - [9(& · Ã) –÷(¥9)]

A: In vector calculus, gradient and divergence are very significant. The operator ∇→ is used to express…

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A: 1/(2πi) * ∫_c-i∞^c+i∞ r^(-ρ) * (sin ρθ)/(sin 2ρα) dρ = (1/(2α)) * (r^n * sin nθ)/(1 + 2r^n * cos nθ…

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A: Given: I=∫5tan2xdx We know that 1+tan2x=sec2x…

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Q: Evaluate the following (i) (ii) L{t? et cost} Use convolution theorem to evaluate 4 (s2+2s+5)²)

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Q: (b) Use part (a) and find the expansion of the following cos x, and x2. - 1 + cos x

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Q: 2) Evaluate: x* cos(x 5) dx. (A) 1/4 sin(x 5) + C (B) 1/5 sin(x 5) + C (C) sin(x 5) + C (D) 1/5…

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Q: The function (f) with a period of 2π is defined by: f(x) = cosh (x - 2π)  if x∈[π ; 3π] a)…

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Q: Use the product to sum formula to evaluate cos 11tt/12 cos t/12 (2+v3)/4 -(2+v3)/4 O (2+v3)/2…

A: This question is based on trigonometric formula.