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: 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: 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: 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: 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: 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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