Determine the types of all the isolated singularities of the following functions and compute the residue at each isolated singularity V where √ is the principal branch of z. (a) tanz; (b) cosz-¹, (c) Log), (d) (z²+1)2,

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Q: 4. Find the Laurent series of f(z) = 2 at 20 = 0 and residue Res(f(z); 0).

A: Given  fz = 1 + 2z2z5 + z3                          ⇒  fz = 1 + 2z2z3z2 + 1…

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A: Given function f(x) = 10x4 - 60x2 = 10x2(x2 - 6)

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A: Statement: If two square matrices are similar, then they have same eigen value

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Q: Every submodule and every homomorphic image of a semi-simple module is semi-simpl

A: Every sub-module and every homomorphic image of a semi-simple module is semi-simple

Q: 1. Find two roots of the equation f(x) = 2x³ -7x+2. Use Fixed point Iteration.

A: Given equation is  f x = 2x3 - 7x +2                  f 0 = 2 > 0                  f 1 = 2 -…

Q: T: R² R³ T([₂2])- X2 = T ¹([3³])= 2x₁ + x₂ 5x2 La₁ - 2x2 Ex: 5 Ex: 5 Ex: 5

A: Put x1=-3,x2=4 2x1+x2=2(-3)+4=-2 5x2=5(4)=20 x1-2x2=(-3)-2(4)=-11

Q: 2S-1/2 √-²²2². (a) Which of the following statements best describe the given integral? O It's a Type…

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Q: 2. Let A = {a, e, g, i, s}, B = {g, i, m, o, p, y}, and C = {a,b, o, r, t}. Find each of the…

A: Sets:A=a, e, g, i, sB=g, i, m, o, p, yC=a, b, o, r, t

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A: Since you have posted a multi subparts question according to guildlines I will solve first…

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Q: Find all Solutions to the matrix equation A·B = B.A wheRe A = [X _Y] and B= x-1 ]

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A: The surface f(x,y)=yx at the point (1,2,2) we use the formula z=z0+(x-x0)fx+(y-y0)fy

Q: Let T: R² → R² be defined by T = {[5].[a]} C= Given Pc 1 -2 = [223] -2 5 [T](PB (u)) = Ex: 5 ([2/2])…

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Q: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty…

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Q: Differentiation. Find the value of the derivative of (iz³ + 15z²)³ 3 at 10i. [(iz³+152²)³] -405000…

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Q: 1 V2T 1 le -1 e -1/2x²dx

A: We know that Taylor's series for the function ex is given by  ex=1+x1!+x22!+x33!+…=∑n=0∞xnn!.…

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Q: Suppose h E L¹(R). Prove that for every c> 0. 3 |{bER: h* (b) ≥ c}|≤||||₁

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Q: Given [T]g = P(T(u)) Pc(T(u)) = -3 0 0 Ex: 5 30m -2 0 3 —1 | , use the Fundamental Theorem of Matrix…

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Q: 2.2 Obtain g(t) if G(³) = 5 + 25 +6 S 5 (5+1) ² (5+2) 3.) Find g(t) given that G (S) = 10 (5+1)(65²…

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Q: of Logarithms Use the properties of logarithms to expand the expression. log_(5)((3)/(7))

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Q: -2 2 07 C=015 -235. C has a pivot position in every row. (ii) -C has a pivot position in every…

A: As per student guidelines I solved part (iv),(v),(vi)