Suppose that f = u+ iv is analytic in a domain D. Show that the Cauchy-Riemann equations in polar coordinates (r, 0), where I = r cos 0, y =r sin 0, are given by dv ar ne

Q: 4x-y<-1

A: Given  4x-y&lt;1 Can be rewritten as y&gt;4x-1 So we take the area above the line y = 4x -1 And all…

Q: 5. Evaluate: tan-(2 – 3j). Express in polar form

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Q: 5. Find two sets of polar coordinates for the Cartesian point (-7, 7/3) such that 0<0<2T.

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Q: determine the slope of the tangent line to the polar curve r = 1+3 cos(20) at 0 6

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Q: Sketch the curve with polar equation r = cos(3θ), 0 ≤ 0 < 2π, plotting only the points with r≥ 0 and…

A: The given problem is to sketch the given curve with polar equation r=cos(3theta) for 0&lt; theta&lt;…

Q: 7. Find all points of intersection of the r= 3sine polar curves: such that r= 1+sine

A: We equate the two equation to find solutions.

Q: 6. Convert 5,5/3] to polar coordinates with r positive and between 0 and 27

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Q: Let (r, θ) denote the usual polar coordinates. Show that if U(r, θ) is a harmonicfunction, then so…

A: The objective of this question is to prove that if U(r, θ) is a harmonic function, then V(r, θ) =…

Q: A particle is moving in the plane, so its coordinates and y are functions of t, and its polar…

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Q: Sketch the graph of r = a(1 – cos8) In polar coordinated , assuming a is a positive constant Is 2.…

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