Q:9 Evaluate cot(72)\dz 3 [z e? + by Cauchy's residue theorem.

Q: 3 e flow in the field F = 4i + 9j + 2k along the path C, where C is the curve r(t) = 7 cos 4ti + 7…

A: Solution

Q: z2 – 1 What is residue of f (z) = at z=3 ? %3D 8. Res (f(z),3) = 3 %3D None 8. Res (f(z), – 3) = %3D…

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Q: (a) Suppose X U (0,n), where n is a positive integer X-[X] U (0, 1). (b) Use the result of (a) to…

A: De Moivre's theorem gives an axiom for computing the powers of complex numbers. We first gain some…

Q: 59. Prove the general formula iwollo oi ons dx 1 x - In x – b + C %3D (x – a)(x – b) a – b - - where…

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Q: By the odd extension method applied to the function f(x)=e-2=, where r > 0, the Fourier integral of…

A: Given function fx=e−2x where, x>0 We have to find the Fourier integral by the odd extension…

Q: Q2= A) for E= 2xĭ-3Y3+K %3D prove That divc curl È)=0 %3D

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Q: e (²+1)5 sin f(z) = sin ³ z 2³(2-3i)² # Compute the residue Res(f; zo), where zo is the pole.

A: Given that f(z) = sin 3 zz3(z - 3i)2 e1(z+1)5sin 1z-1

Q: TQ residue of f(z) = e (z – 1) (z + 9) at z = -9 is 10e-9 :Select one True False

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Q: 4.3 Use the calculus of residues to evaluate the following integral r27 1 1+8 cos? 0

A: We find the given integral by using calculus of residues.

Q: Use the residue Theorem to show that T Cosh 7 2 sinh 7' 2 sinh² 7. 22 -1 -dz 3Di Se (22 + n²)² sin z…

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Q: (b) The For any X1,...X, and Y1,..., Ym, we have: n п т Cov EXi, -ΣΣCον (X, Y) i=1 j=1 i=1_j=1 Hint:…

A: From the property of covariance,  Assume that X and Y are the random variables. Therefore,  CovX,…

Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

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Q: z2-1 What is residue of f (z) = at z=3 ? %3D None -8 Res (f(z),3) = 3 %3D 8. Res (f(z),3) = %3D 8.…

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

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Q: Which of the following is true about I = f. -2i+3e2z dz? (z+7i)8 I=0 by Cauchy Integral Formula…

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Q: Determine Taylor's formula of order 1 and center a = (0, 0) of f(x)=ex1sin(x2).

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Q: التاريخ اليوم موضوع الدرس A) Discuss the conrergence of facx) %3D on A = Co,0)

A: Convergence of the sequence

Q: Detemine the x-values at whìch, 9水)= 2xー 3xー+X メt,xE - スxナラメー3x underined. Evaluate the linit ac…

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Q: z2 – 1 What is residue of f (z) = at z=3 ? z (z – 3) None -8 Res (f(z),3) = 3 %3D Res (f(z), – 3 8…

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Q: Let 1973 - sinh(1/(2z)) and : (0, 27]→C, Then, (t) = 3 cos(t) - 13 sin(t) %3D 2Ep1070 1971 |F(z)dz =…

A: We have to evaluate the complex integral ∫γfzdz, where the complex function fz=1z-2+sinh12z. First,…

Q: HW klx) = 2x+5 ㄱ 1. Find ke-¹(x) 2. Prove by kokorklok

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

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Q: ax² + bx+c, g(x) = -ax² + bx+c, where ac # 0, th hat f(x) g(x)=0 has at least two rool roots

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Q: CF d? for the veder field compute Cis the line segment from Co.o) to Cl,3) ìs where

A: Step:-1 Given that F→=1+x2, xy2 and C is the line segment from 0, 0 to 1, 3 parametrization the the…

Q: 8. Verify that the function u(x, y) = eª sin(y) is harmonic in the region where it is defined and…

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Q: d. Find the zem and its orkr for the finction f(z) = 1- ni + z+e.

A: Givenf(z)=1-πi+z+ezTo calculate zereos and order of f

Q: Express the limit lim E (4 cos (272;) + 6)A¤; [2, 4] over as an integral. n- 00 i=1

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Q: ▼ 3.1. Use Cauchy-Riemann equations to prove that ƒ(z) = z² is differentiable at z = zo E C.

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Q: do Evaluate the intergal using the residue theorem. 12 +1 cos 0

A: ∫02πdθ12+1 cosθLet, z=eiθ . Then cosθ=(z+z-1)/2, dz=iz dθ, so that∫02πdθ12+1…

Q: 2. Find a closet rank-1 approximation in the f norm to A = cos 8 - sin e sin e cos 0

A: According to the given information it is required to find closet rank-1 approximation in the l2 norm…

Q: Z +1 f(z) %3D (z – 1)? (z – 2) what will its residue at z = 1? %3D

A: Introduction :

Q: 7. a) Prove that for r > 0 * (E) + c. Vr2 – r²dx = vr² – x² + -1 sin 2 +C.

A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

Q: 4.3 Use the calculus of residues to evaluate the following integral 27 1 1+8 cos? 0

A: We have to solve the integral by residue formula

Q: (b) If u =x cosy+ ye», where x=s+2 and y= st, prove that 2- ds du - (s - 21) (* siny-xye -e").

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Q: 1)the f a) 3 cosh z b) 0 c) in d) n -dz by using the residues is equal to

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Q: 2 de Evaluate the intergal using the residue theorem. 12 + 6 sin 0

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Q: - Using Euler's equation, show that- : z fain (K 0)} - z sin Ø z2 – 2zCos Ø +1

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Q: Let z= 28x + 32xy - 8y , where x(t,s) = cosh (4t) cos (5s) and y(t,s) = sinh (4t) sin (5s). ze at…

A: Here, z=28x2+32xy-8y2

Q: |1) Use a sine expansion to compute the solution of ( ди д'и at ôx? u(0,t)=u(1,t) = 0,t > 0, u(x,0)…

A: According to the given information, it is required to compute the solution of the given equations.

Q: 31. f sen z - sen z dz tag z dz dz cos z -In lcos z + C = In jsec z + C %3D %3D cos z

A: Topic- indefinite integration of trigonometry function

Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where - -] b. A =…

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Q: ZH E LI and HI 1 GJ. Complete the proof that AGIJ S AGHJ.

A: Here we use two concepts  1) sides opposite to equal angles of a.         triangle are equal. 2)…

Q: 27 de Evaluate the intergal using the residue theorem. 13 +4 sin 0

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Q: 4.3 Use the calculus of residues to evaluate the following integral 2m 1 de. 1+8 cos? 0

A: We find the given integral by using calculus of residue.

Q: 1 And the radios of Co for the pover Serie for the Power Serie vergence 00 xh (2"+1) (n?+1)

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Q: 4.3 Use the calculus of residues to evaluate the following integral 2 1 1+8 cos? 0

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Q: 1 dz, when C:z| = 1 is Using Cauchy's residue theorem, %3D (z-1)(2+2)2 O a. 0 O b. 27ri Oc. 2ni 9 O…

A: The solution is given as

Q: please solve this question

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