Let C be a simple closed contour |z-2|=3 . Use the extension of Cauchy Integral Formula to evaluate : ze -dz : (i) (1-z)? cos(72) c(z-1)(z' +4) (ii)

Q: Verify that u(x, y) = x4−6x2y2+y4 is harmonic everywhere and determine its harmonic conjugate

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Q: u(x, y) = -e sinx - 2e* siny. Find a harmonic conjugate v of u, namely a function v such that the…

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Q: Find the fay and fyy: f(x, y) = xe" - sin(xy) + x³y

A: fx,y=xey-sinxy+x3y

Q: (b) Verify that the following function is harmonic u(x, y) = −e sin x - 2e-siny. Find a harmonic…

A: Here we have to verify that the function is harmonic and then find the harmonic conjugate.

Q: Let u(x, y) = e=² -y², cos 2xy. (a) Verify that u(x, y) is harmonic in R?. (b) Find its harmonic…

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Q: Let u = e-7*sin(7y). Then a harmonic conjugate of u is

A: If two given functions u(x,y) and v(x,y) are harmonic in a domain D and their first-order partial…

Q: Find V · (V × F) if F(x, y, z) = sin xi + cos(x – 2y)j + 8zk. | V ·(V × F) :

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Q: Bluetop Cab charges $3.20 for the first mile and$1.35 for each additional mile or part of a mile.

A: Given: Bluetop Cab charges $3.20 for the first mile and $1.35 for each additional mile or part of a…

Q: Let F(t) = (- t + 1, t – 2t", - 2t). Find the line (L) tangent to r (t) at the point (- 15, – 24, –…

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Q: F. dr Evaluate So

A: In this question, we have to evaluate the line integral for given vector function along the given…

Q: Find the f(z) = u(x, y) + j v(x, y) for which X b) u = e cosy most general analytic function

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Q: Write the function f(z) = z + 1/z in the form f(z) = u(r, theta) + iv(r, theta) (Answer is f(z) = (r…

A: f(z)=(r+r1​)cosθ+i(r−r1​)sinθ   Explanation:

Q: how that u(x, y) is harmonic in some domain and find a harmonic njugate v(x, y) hen: u(x, y) = 2x –…

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Q: 3. Verify that u(x, y) = x² + 4.x – y² + 2y is harmonic and find %3D - a) the harmonic conjugate…

A: See the attachment

Q: Let r(t) = (sin(t), cos(t), 6 sin(t) + 9 cos(2t)). Find the projection of r(t) onto the xz-plane…

A: Given vector…

Q: Prove that B(m, n) = B(m + 1, n) + B(m,n + 1)

A: given,

Q: 1. Let r(t) = (Vt,t + 2t2, e'). Describe the domain of r. 2. Let r(t) = ((t + 2)-1, sin(t), In(1 –…

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Q: Plot the slope field of y=x+y using slopes m = -3, -2,-1,0, 1, 2. Sketch integral curves for…

A: First we plot the slope field and then plot the curve .

Q: Show that ƒ(z) = 3x² + 2x − 3y² − 1 +i (6xy + 2y) is differentiable at every point in the plan -

A: The given function is f(z)=3x2+2x-3y2-1+i(6xy+2y)...(i).

Q: -2y 2x (x²+y²) ²³ (x²+y²)² Compute fF.dr, where F(x, y) = oriented counterclockwise. (Use symbolic…

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Q: Let f(z) = 5z2 + 3z.  Find u(x,y) if z = 8.2 + 5.9i

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Q: b) (i) Show that dz is a constant independent of z, and R. { Hint : z= Z, + Re"} 1 +- 2z-4 2 -z 3…

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Q: Consider (x, y, z) = 4xy²+ 3y sin(z) and at the point P = (1,2,0) calculate the directions in which…

A: Approach to solving the question:To find the directions in which the…

Q: show that the function 3x²y-y³ ty is he harmonic and then find it's Harmonic conjugate v (x, y)

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Q: u(x, y) = -e sin x - 2e* siny. Find a harmonic conjugate v of u, namely a function v such that the…

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Q: What is the A B (C) D af - of f (x, y) = tan (x²y³ + 2xy)? dy [ sec 2 (x2y3 + 2xy (2 xy + 2y) 2 [sec…

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