(3) a) Prove that the following functions are harmonic and find for each function its harmonic conjugate i) 2e cosy

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Q: b) Prove that if f(z) and f(Z) are analytic in a domain I, then I is a constant function.

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A: Sol:- We can begin by substituting y = 1 - x in the equation of the line to get an equation for x in…

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A: Given differential equation is     d2xdt2+4dxdt+5x=1,  x(0)=1 and x.(0)=1

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A: (a). The straight line that makes equal intercepts on the axes and         passes through the point…

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A: We have used the definition of differentiability to prove 1st part. And given a counter example in…

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A: Sol:- Let P be a point on the rectangular hyperbola xy = c², and let PN be the perpendicular from P…

Q: V Solve using method of undetermined coefficients B dts +6d²x dt2 dx + 12 + 8x =0 when t=0, x==2=-2…

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Q: 4. (a) A finite string of length has the left end fixed and the right end free. The ㅠ initial…

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Q: 1. Let f(x) = 4x5 - 4x³ + 2x² + 3x - 1. Then use Horner's. method to

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Q: Determine (without solving the problem) an interval in which the solution of the initial value…

A: The given equation can be rewritten as            y' + 3tt(t-2)y = t-1t(t-2); y(6) = 1 or,    y' +…

Q: Σ(-1) π n n=1 (n+2)! nath

A: We use ratio test to solve this problem

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Q: Maximize C = 7x + 9y + 6z subject to 12x + 8y + 15z ≤ 72 9x + 8y + 5z ≤ 144 and x ≥ 0, y ≥ 0.

A: We are given: Maximize C = 7x + 9y + 6z subject to 12x + 8y + 15z ≤ 72   9x + 8y + 5z ≤ 144…

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Q: Let be a sequence of functions belonging to L P-space. If this seque is n onvergent, then it is a…

A: Sol:- The statement is true.

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Q: Australia Economy Two sectors of the Australian economy are (1) textiles and (2) clothing and…

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Q: -B-E-B V₂= Let v₁ = 0 2 -5 [B] 2 Av= , and v3 = be eigenvectors of the matrix A which correspond to…

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A: Center lies on x-2y=4.let the center be C(4+2t,t).nowradius r=distance of from the…

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Q: You need a home loan of $65,000 after your down payment. How much will your monthly house payment be…

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Q: Let h(x) = f(x) · g(x), and k(x) = f(x)/g(x). Use the figures below to find the exact values of the…

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Q: Find the length of the chord x² + y² - 4y = 0 along the line x + y = 1.also ind the angle that the…

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