[sin(y)- y2 +1] [x cos(y) 2xy Use your work from question 6 to evaluate: 7) Let F(x, y) = and let C be the curve (t², 2(π - t)), where 1 ≤ t ≤ 2. [ C F.dr

Q: (a) Sketch the graph of F(0) for 0 ≤0 ≤ 2m. F(0) 2 W r = F(0)=1-sin (0) 1 i. Explain and clearly…

A: note :Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: Q3:- Verify that the following functions u are harmonic, and in each case give a conjugate harmonic…

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Q: 5.) Ms. Cyrus has 64 songs on her phone. Two- fifths of the songs are R&B songs. The rest are jazz.…

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Q: Let z = sin(7(z – 2y²)). None of these is true. (-1,1,–4(1– x). A normal to the tangent plane to the…

A: For a function z=fx,y, the tangent plane at point x0,y0 is defined as:…

Q: Evaluate I = f. F. dr, where F(x, y) = (y + sin(x²), x² + e) and C is a circle of radius 5 centered…

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Q: Q1) Verify that the following functions u is harmonic, and find a conjugate harmonic of function…

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Q: Find the length of the curve c(t) defined by c(t) = (-4 cos (t), -4 sin (t), t) if 0 ≤ t ≤ 2л and…

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Q: Show that u = x³ – 3xy? is a harmonic function and find a corresponding analytic function f(z) = u +…

A: To show that u=x3−3xy2 is a harmonic function and to find a corresponding analytic function fz=u+jv.…

Q: Use Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the…

A: We have to evaluate the integral using Green's Theorem.

Q: The function r(t) traces a circle. Determine the radius, center, and plane containing the circle…

A: In this question we will find the radius, center and plane of the circle.

Q: et F(x, y) = (y sin x)i - 3x²j. et D be the unit square (i.e. D = {(x, y): 0≤x≤ 1,0 ≤ y ≤ 1}), and…

A: We have to choose the correct answers of two questions.

Q: is the following function analytic (Express your answer in polar form) f(z): = y - ix x² + y²

A: We can solve this using polar form of analytic function

Q: Q10: Determine the set of point where f(z) = 6z2 – 27 – 4i|z|2 is analytic. -

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Q: (2) Find the work done by F over the curve C in the direction of increasing t. Explain why the sign…

A: Question: Calculate the work done by  Fx,y,z=zi^+xj^+yk^ over the curve  C : r¯t=sinti^+costj^+tk^ ,…

Q: 11. Determine the conjugate harmonic function v of u = re² cos(y) – ye² sin(y) such that f(z) = u+…

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Q: Let f(x,y)=sin(xy)+xsiny be a function of variables of x and y such that x=²+² and y=in. Then ef at…

A: Given: fx,y=sinxy+xsin ywhere x=u2+v2 and y=uv.We need to find dfdu at u=0 and v=1.

Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

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Q: Let C be the closed curve oriented in the counterclockwise direction, consisting of the line segment…

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Q: 3. Use the Fun.Theorem to evaluate F dr, where F = 3xy?ī+ 3x*yj , πί and C is the curve described by…

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Q: = Let Co be the curve formed by the intersection of the surfaces x₁ = 2x² and X3 3x1x2, and let C be…

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Q: Evaluate |-y dx+x dy , where C consist of the curves along the horizontal line from (-4,4) to (-2,4)…

A: The given integral is: ∫C -ydx+xdy Where C consists the curve along the horizontal line from -4,4 to…

Q: Which of the functions describe the sinusoidal graph below: f(t) -1 a. f(t) = u(t-π/4) sin(t - π/4)…

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Q: Let C be the curve defined by r(t) [6 cos(t) – 5 cos (t), 6 sin(t) – 5 cos(t) sin(t), cos(t)] for 0…

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Q: Let z be a function of x and y defined implicitly from the equation 9ye" - 5 cos(y+ z – 1) = 7x –…

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Q: 2. Let f be the function f(x)= arctan.x. (a) Find the third Maclaurin polynomial for f. (b)…

A: To find the maclaurin polynomial for f.

Q: Consider the function. f(x, y) = 9 - E COMITEE (b) 0 = Find D f(2, 7), where u = cos(0)i + sin(0)j.…

A: Given function:- fx,y=9-x7-y4