4) If V is the imaginary part of an analytic function f then an analytic function with real part vis a) 1/f b) -if c) If d) -f e) NOTA 5) If v is harmonic conjugate of u then a harmonic conjugate of vis a)-iu b) iu c) u d)-u e) NOTA

Q: √2 2. Consider the polar curves C₁:r = 4 + ³√² cos 0 and C₂: r = 2 - ² cos € as shown in the figure…

A: b. Consider the given polar curves, C1:r=4+322cosθ and C2:r=2-222cosθ the diagram is shown below,…

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A: find the volume of the solid generated by revolving the area bounded by the given curves about the…

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Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

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Q: 3. Let A and B be sets in the universe U.Prove the following statements: (a) A = A. (b) AB if and…

A: Solution :-

Q: Let S be the quadric with equation 4x² - (y - 3)² + 4z² = 4. What type of quadric is S? Find an…

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Q: 10x + 2y — z = 27 -3x - 6y + 2z = -61.5 x + y + 5z = -21.5 L == Answer x = y = U = N ||

A:

Q: II. Consider the polar curves C₁ : r = 3 (in blue) and C₂:r = 2-2 sin (in red) and let R be the…

A: Given,C1 : r =3C2 : r =2-2sinθand r > 0 , θ∈[ 0, 2π )

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Q: Problem 25. Find the Laurent expansion of f(z) = 1/[2(2-1)(z-2)] in i) 0 < |2|<1 ii) 1<|z| <2 iii) 2…

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Q: Find the daigram only for the equation  z =x^2+y+cos(x^2)+siny

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A: Numerical programming for the given numerical problem is given as,

Q: 3. Let zo be an isolated singularity of f. Then Res(f'(2), 20) =

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Q: 1. Evaluate the following iterated triple integrals: pa+ay (a) f f f xy dz dy dx 1 (6) L L L (x² +…

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Q: Let S be the surface with equation 4y² + 4z² - x² - 16 = 0. 1. Find an equation of the trace of S on…

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Q: #1. Let C be a space curve defined by the vector-valued function R(t) = (sint cost, sin² t, √√3t).…

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Q: c) y (3) - 54 (²) +254² - 1254 x(esx 125)+25

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Q: (a) The eigenfunctions of the following eigenvalue problem: X" + XX=0, X(0)= X(x)=0 are given by…

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Q: Let (R, +,-) ring with properties X.XX, XER Cindempotent properties), show! @a = 0, x ER (b) x. y…

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Q: or problems 1 - 10 refer to these sets:  U = {a, b, c, d, e, f}     A = {a, c, e, f} B = {c, d, e}…

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Q: Question 4 4.1. Find a power series representation for the function 2x-15 sign, 4.2. determine the…

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Q: Let S be the surface with equation 4y2 + 4z²x² - 16 -0. 1. Find an equation of the trace of S on…

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A: We need to find the determinant of the given matrix using raw operations and cofactor method…

Q: III. Let S be the quadric with equation 4x² − (y − 3)² + 4z² = 4. a. What type of quadric is S? Find…

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Q: For every real m x n matriz mx m) and a diagonal m x n matriz

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Q: x² A quadric surface is defined by the equation: + 3y² = 3 + z 3 1. Solve the equation of the traces…

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Q: Consider the polar curves C₁ : r = 3 (in blue) and C₂: r = 2-2 sin (in red) and let R be the shaded…

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Q: 3 III. 1. Using the technique in Item II., find the general solution of the system ty' = 2 3 2.…

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Q: (D³ + 4D² +9D + 10)y=-24e-* when x = 0, y = 0, y'= -4, y" = -10 ANSWER: y = e-2x + excos (2x) -sin…

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A: Solution:-

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Q: het Ley) = y(4) + y (3) _ 7 y (2) _y (¹) al solve: Lys = 36t-24et > b) solve: hy)= 36t-24et 2.2t c)…

A: