For the following u(x, y), show that it is harmonic and then find a corresponding v(x, y) such that f(z) = u+iv is analytic. u(x, y) = sinx coshy

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: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

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Q: Given that v(x, y) = ye* cos y + xe* sin y is the imaginary part of an analytic function f (z). Show…

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Q: Identify and sketch the domain of sin-'(y – 2x) V1- x f(x, y)

A: Given f(x,y)=sin-1y-2x1-x

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: Q2) Find az/du and äz/au for the following function and then find dz/ou and az/dv at the given…

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Q: Q2] Find the analytic function F(z) if u = coshy.cosx, (B.C. v-0 at x=0)

A: at

Q: valuate f (z) dz.where C is the parabola y =x2 from z =-1+i ti 7 = 1+i and S (z ) = 6.x

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Q: Find fxxx for f(x, y) = Sin() at (π, π)

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Q: Solve the DE by eliminating the arbitrary constant of x sin y + (x^2)y = C

A: Given that the expression xsiny+x2y=C. Differentiate with respect to x.…

Q: The directional derivative of f(x, y) = e²y - x at the point (1, 2) in the direction indicated by…

A: In this question, We want to find the directional derivative in the given direction.

Q: (z)dz

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Q: f(x, y, z) = x + tan(yz) exyz + 1

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Q: Write the function f(x,y) = xcosh(x)cos(y) - ysinh(x)sin(y) + i(xsinh(x)sin(y) + ycosh(x)sin(y)) in…

A: f(z)=Re(z)cosh(Re(z))cos(Im(z))−Im(z)sinh(Re(z))sin(Im(z))+i(Re(z)sinh(Re(z))sin(Im(z))+Im(z)cosh(Re…

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: Determine if the following functions are analytic or not: 1. f(z) = (z* + 1)³ – 3z* where z is the…

A: (i) The  given function is ;               fz = z*+13 - 3z* We know that a function  f is analytic…

Q: Find the derivative of f(x, y, z)=x²-xy² -z at the point p (1,1,0) in the direction of V=i-j+2k (it…

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Q: Construct an analytic function of the form f (z) = u + iv, where v is tan- (y/x), x # 0, y # 0

A: f(z)=u+iv where v=tan-1(yx)  We need to find the analytic function f(z)=u+iv  we apply Milne Thomson…