3. Use the Fun.Theorem to evaluate F dr, where F = 3xy?ī+ 3x*yj , πί and C is the curve described by r(t) = (t + sin())i + (t + cos())j, 0

Q: Q15) A complex-val functio is given in the following. f (2) = %3D a) Find real (u (x, y)) and…

A: Here we use definition of existence of limit to check  f(z) is continuous or not.

Q: find its harmonic conjugateu andd find analytic funchionf(2)=utiV sätisfying the Indicated condition…

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Q: +++++ ++ + 2 riecononi ni bilw no elV us led (Jq 1) () ++++ dordw go alnoji vas da 1 (1g 1) (b) YOe…

A: follow next step

Q: Pr. #14) Find and sketch the domain of the function in R2. In [sin- ()] (x, y) x2+y² %3D -

A: This is the problem of multi-variable functions.

Q: 5. Let f(2)=. Use the polar form of the Cauchy-Riemann equations to determine where f is…

A:

Q: a) Use the definition of the hyperbolic functions to prove that 2cosh?(x)–1=cosh(2x). 1%3D

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Q: Fineling the derivative of trigonometric %3D

A: Given:  f(x)=ln(2+x )

Q: Find T', N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 4t) at the point t = 0

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

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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: (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: Find 7, Ñ and B for the curve (t) = (4 cos(3t), 4 sin(3t), 2t) at the point t = 0 Give your answers…

A: We have to find the  for the given curve.

Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: Let f be a function which has an inverse and let f(-1) = 2. If Q is the surface of revolution…

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Q: Find the domain of the vector function 7(t) = Domain: {t| <t< }

A: