Verify the line integral and surface integral by relating them to the Stokes' Theorem where C is the circle x² + y² = 1 on xy-plane with a counterclockwise orientation looking down the positive z-axis. [x²ydx + xdy

Q: find the tangent plane to the surface z = Vy-x at the point (1,2,1)

A: Equation of tangent plane is z-c = df/dx(x-a)+df/dy(y-b) at point (a,b,c)

Q: Use Stokes' Theorem to evaluate F. dr. F(x, y, z) = z²i + 32xj – y°k - where C is the circle x? + y?…

A: Given Fx,y,z=z2i+32xj-y3k. Let C be the circle x2+y2=1 in the xy plane with counterclockwise…

Q: Identify the surface for ρ = 4 cos φ

A: The given curve is: ρ=4cosφ Multiplying both the sides by ρ: ρ2=4ρcos φ Now, converting it into…

Q: 28. fc[(y – 2) dx + (z – x) dy + (x – y) dz]; C is the curve of intersection of x² + y? = 1, and a +…

A: The stokes theorem states that ∮CFdr=∬D∇×Fds. The given integral is: ∮Cy-zdx+z-xdy+x-ydz, where C is…

Q: Verify the Stokes' Theorem in evaluating F.dr if F(x, y, z) = z² i + 2xj- y³ k, where C is the…

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Q: H.W: find the tangent plane to the surface z = Vy -x at the point (1,2,1)

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Q: Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3…

A: Let C be a smooth curve and r→t=xti^+ytj^+ztk^ be the position vector of any point x,y,z on C.…

Q: Use polar coordinates to integrate under z=xy above the first quadrant of the unit circle on the xy…

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Q: Find an equation of the tangent plane to the surface z = 2y² – 3x² at the point (-3, -3, -9).

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Q: Use Stokes' Theorem to evaluate F. dr. F(x, y, z) = 2²i + 26xj – y°k | where C is the circle x2 + y²…

A: The objective is to find ∮CF.dr using Stoke's Theorem. Where F(x,y,z)=z2i+26xj-y3k and C is the…

Q: Let F = Use Stokes' Theorem to evaluate с شرح = F. dr, where C is the curve of intersection of the…

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Q: Find an equation of the tangent plane to the parametric surface Ř(u, v) = : ((u — sin u) cos v, (1 −…

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Q: Find the equation of the tangent plane to the surface z = 4.x*y? + 2y at point (1, -2, 12).

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Q: 2. Find an equation of the tangent plane to the parametric surface F(u, v) = (, 2uv, uv?) at the…

A: (2) Consider the provided question,

Q: Use Stokes' theorem to evaluate dr where = (yz, 2xz, exy) and C is the circle x² + y² = 16, z = 4,…

A: We have to evaluate  where  and  is the circle  viewed from above

Q: Let F =< xy, 7z, 4y: Jo C Use Stokes' Theorem to evaluate F. dr, where C is the curve of…

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