Use Stokes Theorem to find the circulation of F= (xy, yz, az) around the boundary of the surface S given by z= 16-2² for 0≤x≤4 and -2≤ y ≤ 2, oriented upward. Sketch both S and its boundary C. Circulation = [F. dr =

Q: Let F = 4ai + 1yj and let C be the closed path around the circle x² + y² = 9, traversed once…

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Q: Ja² xz ds, where C₁ is the curve defined by Ŕ(t) (Int, 3-4√t, 2t), te [1, 2]. Evaluate

A: Given:  Curve C1 defined by R→t=lnt,3-4t,2t , t∈1,2. To find: ∫C1xzds.

Q: a) Find the tangent plane and normal line of the surface f(x, y, z) = x2 + y?e* + z? = 3 at point P…

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Q: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u ER…

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Q: Let F(x, y) = (cos(x*) -v°)i + x*j. F• dr, where C is a curve consisting of the line segment joining…

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Q: Q1: Find the tangent plane and normal line of the surface F(x,y,z)=x² +n + y² + z² = 10 at point…

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Q: Find the Jacobian ∂(x, y) ∂(u, v)for the indicated change of variables. x = 3uv,  y = 2(u − v)

A: on solving this we get the

Q: Let f(u, v) be a differentiable function with f(-1,3)=0, fu(-1,3)= 2 and f(-1,3)= -3, g(x, y, z) =…

A: Given that f(u, v) is a differentiable function with f-1,3=0, fu-1,3=2 and fv-1,3=-3,…

Q: Answer the following True or False: Let f(x, y) be differentiable at (zo, 30). Then the vector is a…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: Hand written plzzzz...asap

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Q: Sketch the contour map of the function f(x, y) = 4 – Va2 + y? Label the level curves at c= 4, 3, 2,…

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Q: SET UP an iterated double integral that will give the volume of the solid 3xy over the region R on…

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Q: Let S be the downward-pointing cone whose base is the unit circle in the ry-plane centered at the…

A: Here given that unit normal vector is outward sence,that is if  be the unit normal vector to the…

Q: Let F(r, y,z) = where r2 + y? < 4, oriented by the upward normal. (r,-z,2y(r2-y²)). Find ff, F- dS…

A: Given Fx,y,z=x,-z,2yx2-y2and S is the saddle surface z=x2-y2, where x2+y2≤4, oriented by the upward…

Q: Use Green's Theorem to calculate the circulation of F = 3xyi around the rectangle 0 ≤ x ≤ 2,0 ≤ y ≤…

A: By Greens theorem ∫C[Pdx+Qdy]=∫∫R[∂Q∂x-∂P∂y]dxdy, where R is the region bounded a simple closed…

Q: Let f(u, v) be a differentiable function with f(0, 2) = 0, fu(0, 2) = 2 and f(0, 2) = -3, g(r, y) =…

A: Introduction: The chain rule of the partial derivative is used when the multivariable function is…

Q: A normal vector to the tangent plane for the surface z = , at the point (1, 1, 1) is: y - Select…

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Q: Draw a contour plot for f(x, y) = xy. Include contour lines at z = ±2, ±1, 0. On top of this contour…

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Q: |Let g(s) = e°(s4 + 6). a) Find the equation of the tangent line to g at (0, 6). y = b) Find the…

A: Differentiate at given value and then use formula of tangent and normal line

Q: Find the gradient vector, Vf, for the function, f(x). f(x, y) = x²y² + ex²y b. f(x,y,z) =x²y*…

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Q: Let → F = . Use Stokes' Theorem to evaluate SSS curl → F.d S, where S is the hemisphere x^2 + y^2 +…

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Q: Calculate ff f(x, y, z) dS For Part of the surface x = z³, where 0 < x, y ≤ 8 - 1²2 ; f(x, y, z) = =…

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