Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.  F = sin 3y i + cos 7x j; C is the rectangle with vertices at (0, 0),(pi/7,0),(pi/7,pi/3)  and (0,pi/3)     a) 0   b) 2/3π   c) - 2/3π   d) -4/3 π

Q: Use Green's Theorem to compute y dx+(x³+3xy²) dy where C is the closed curve around the triangle…

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Q: If f(z) is analytic function expressed in polar form, show that: (sin + icos) of ᎧᎾ f'(z)=(cos- i…

A: To show that the derivative of an analytic function f(z) in polar form is given by:we'll use the…

Q: Show that the work of F = (2³-y³)i + (2³-y³)j on c, the unit circle centered at the origin with…

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Q: Find a critical point [.xo. yol of the function f(x, y) = -2 + x² - 64 y + 6 xy + y². [xo. Yol =…

A: The given function is .The aim is to find the critical point and the nature of the critical…

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

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Q: c) Use Stokes' theorem to evaluate F. dr where F = z' i+yJ + xk and C is the triangle with vertices…

A: Stokes theorem is used to find the line integral of the vector point function

Q: Find the Laplace transformation of the unit impulse function 8(t-22017) and The unit step function…

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Q: Q. Let f(z)= u(xy)+ i V(x>Y) be analytic function and Z= re Find the Cauchy - Reimann eguations in…

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Q: h) Find a parametric representation of the Parabolic equation z = 9(x² + y²)

A: Parametric representation of the Parabolic equation z = 9(x² + y²) will be cartesian coordinates as…

Q: QUESTION 1 a) Evaluate the line integral F. dr in terms of a where F = cos yi + rj+ ye*k and C is…

A: Work done by the force is the line integral from initial point to terminal point. A force field will…

Q: A) Show that the function u(x; y) = 5x4y - 10 x²y³ + y5 is harmonic and determine the harmonic…

A: (A)

Q: QUESTION 3 Calculate OF.dr if F= and C is the triangle oriented counterclockwise with vertices at…

A: please see the next step for solution

Q: b) For the curve r = 2(1 - sin 8) i) Sketch the curve ii) Find the horizontal tangents to the curve

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Q: Consider the curve C shown in the attached figure, which is the intersection between surfaces S, and…

A: To parameterize the curve which is the intersection of the below curves in the first octant.…

Q: A curve is given in the parametric form x = [(2x - 1)/ (t + 1)], y = [t / (t+ 1)], z = t + 2. Find…

A: According to the given information, it is required to determine the torsion of the given curve.

Q: Z F(z) FCZ) = e CZ-1) Sin (1) find and classify zeros and Singularities

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Q: 3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with…

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Q: 19. Find y' in the parametric equations x =, t-1 t+1 A) (f – 1) 7-1 B) (1+ 1)? 2 +1 C) (1+1)? t +1…

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Q: b) Find v²f where f = e²x sin2y. cl Write the sufficient condition for ovistence of Lapla

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Q: Let F = . [F Use Stokes' Theorem to evaluate F.dr, where C is the triangle with vertices (7,0,0),…

A: Given,             F→=4x+y2, 8y+z2, 9z+x2, Use Stokes' Theorem to find:                ∫CF→·dr→,…

Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: a) Find the Laplace transformation of the function f(t) = cosh at sinh bt

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Q: Let R be a vector function such that T(t) Find The moving trihedral to the graph of R at t = 0. = co…

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Q: V × (V × F) = V(V-F) – V°F. %3D

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Q: Let u = 2i - j, v = 4i + j, and w = i + 5j. Find specified scalar u . v + u . w.

A: We will apply dot product of vectors.

Q: Let F = SOFF Use Stokes' Theorem to evaluate . dr, where C is the triangle with vertices (6,0,0),…

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Q: Let w where z = rei0. 1) Show that by using Cauchy Riemann Equation (C.R. Eq.) in polar form that w…

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Q: g) Find the Fourier sine series of the function f(x)=-100¹0(-<x<n); f(x)= 100¹0 (0<x<n)

A: We have to find the Fourier sine series of the function  f(x)=-10010if -π&lt;x&lt;010010if…

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

A: To find- Use Green's Theorem to evaluate ∫CF·dr. (Check the orientation of the curve before applying…