Suppose F(2, y) = (2x – 4y)i + 5æj and C is the counter-clockwise oriented sector of a circle centered at the origin with radius 4 and central angle 7/6. Use Green's theorem to calculate the circulation of F around C. Circulation = 2pi/9

Q: et R={(x,y)=R² | x² + y² ≤4y}. Draw it. Write it in polar coordinates.

A: R=x, y∈ℝ2|x2+y2≤4y

Q: Let u = u(x, y), and let (r, 0) be polar coordinates. Verify the re- lation |V? = u; + zuổ Hint:…

A: Let u = u(x, y) and let (r, θ) be polar coordinates.

Q: 4. First, sketch a picture of the line which passes through P = (1, 1, 2) that is perpendicular to…

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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: Consider the parametric curve 5 + cost y = 1+ sint. x=

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Q: A circle C in the plane x + y + z= -6 has a radius of 6 and center (- 2, - 3, - 1). Evaluate F•dr…

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Q: Determine the parametric equations of the flow lines for the velocity vector field, v, where v =…

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Q: Find the circulation f V. dR, where V = yi + (x² + y²)j + (x + y)k, and C' is the triangle with…

A: In this question we will find the circulation of

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Q: Evaluate /| cos(x? + y²) dA, where D is the D disk x? + y <I Select one: a. -n O b. A O c. O O d. 2…

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Q: 15 Practices :- Find the polar egatin for the fotlous radius and Center of the cincles:- O radius…

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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: find curl (grad Q).

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A: The curve is  r=12θ ;0,2π The table with the values  θ 0 π4 π2 π 3π2 7π4 2π r 0 0.392 0.785…

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Q: Prove that o curl f· dS = f pf • dr - f v o xf - d$ %3D

A: