Use Stokes' Theorem to find the circulation of F = (xy, yz, xz) around the boundary of the surface S given by z=9-² for 0≤x≤3 and -4 ≤ y ≤ 4, oriented upward. Sketch both S and its boundary C. Circulation =

Q: →> Let S be the surface in R³ that is the image of the function F: R² R³ given by F(u, v) = (u²,…

A: The given surfaces are Fu,v=u2,v2,u+v and 2x2+y2+z2=7. To show that the point 1,1,2 lie on both the…

Q: Consider the rormal line to the surface z= z + y? (parabokoid) at the point P(1,1, 2) Find the point…

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Q: II. Solve the differential equation 1. xy'dy-2y+x*dx = 0

A: We solve the first DE. *By Bartleby policy I have to solve only first one as these are all unrelated…

Q: 7. Parallel flow. Sketch and interpret the flow with

A: Given,          Fz=z

Q: = Let x: R? → R³ be the function given by x(u, v) = (u cos v ,u sin v , bv) 1. Check whether x is…

A: (1)Given that:x:R2→R3 is the function given by x(u,v)=(ucosv,usinv,bv)In order to check the proper…

Q: Q6|| Find the tangent plane and normal line of the surface x+y+z=1 at the point p(0,1,0).

A: Equation of tangent plane is Fx(x-x0) +Fy(y-y0) + Fz(z-z0) =0  F = f(x, y) =k

Q: Let S be the surface of the sphere of radius 6 centered at the origin, and let F(z, y, 2) =…

A: Let S be the surface of the sphere of radius 6 centred at the origin. Let F(x,y,z) = x3zi…

Q: the y-axis direction

A: Given: f(x, y)=ex lny5 at point (x, y, z)=( ln2, 5e, 2) To find: The slope in the y direction.

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

A: We have to calculate partial derivatives first.

Q: Use Stokes' Theorem to calculate rot F dS, where F = ri + yj + rk and S is the surface given by the…

A: This is a problem of vector calculus. By using stokes theorem formula we will evaluate given…

Q: Example: find the tangent plane and normal line of the surface f(x, y, z) = x + y' +z-9=0 at the…

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Q: Show that tan²t+ cot2 t = 1 is a a² possible form of the boundary sur face o aliquid and find an ex…

A: If we take f(t)=tan2 t  then it is proved  evidently that the given F(x,y,t) is a possible form of…

Q: Find the equation of the tangent plane at the point - 2 of the surface * = 0 3, y = yo z = f(x, y) =…

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Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: Evaluate F.dr, where F (x, y, z) = - yi + xj + z*k and C is the curve of intersection of the plane y…

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Q: What is a unit normal to the surface xy + 2x

A: Given, the surface x2y+2xz=4    at  the point (2, -2, 3)

Q: Let C be the curve y = 5x for 0 <x < 2.2. %3D 50 45 40 35 30 25 20 15 10 5- 0.5 1 1.5 Find the…

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