Use Stokes theorem to evaluate ff.curl F.nds. where F = (xyz, x, e* cos z), while S is surface x² + y² + z² = 9 for z ≥0 with upward orientation. ms: 257

Q: 1. Let k be a nonzero constant. Show that the equation of the tangent plane to the surface xyz = k…

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Q: O Calcalate the integea/ over the giren region by dhangng to polar cocalinater fcx,y) = 14xy/;

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Q: Find the equation of tangent plane to this surface at the point where x :1 and y = -1.

A: Given surface is z=f(x,y)=sin(π (3x+2y)) +x2y2 Equation of tangent plane is given by,…

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (-4, 2, -44).

A: The solution is given as

Q: Assume S is the surface x1000+y8000+z1000 = 10¹2 and f = (9+ eyz, x³yz, 3x - 5y - 6 cos(zx)).…

A: Here we use the Divergence theorem for a surface S inclosing a volume V

Q: Evaluate SF. ds where F = (3xy², 3x M M is the surface of the sphere of radius 3 c the origin.

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Q: a) Consider the surface z = Find the tangent plane to the 3. surface at the point (4, 3, 5). (4.04)3…

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Q: Use Stokes's Theorem to evaluate f.7 X F.dŠ, where F (x, y, z) = (y +29)î – xj + x³yk and S is the…

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Q: Įsin x cos^(3/2) x dx * O -2/5 cos^(5/2) x + C O None of the choices -5/2 cos^(5/2) x + C O -2…

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Q: Consider the surface z = 2 – xy in R³. Use the second derivative test to find the points on this…

A: Given curve z = 2-xy To find :- Use the second derivative test to find the points on this surface…

Q: Evaluate fS (3x + 4y²)dA by changing it into polar coordinates over the region in upper half plane…

A: In polar coordinates

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

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Q: a. Sketch the surface x2 - y2 + z2 = 4. b. Find a vector normal to the surface at (2, -3, 3). Add…

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Q: 3 Reverse the or der of intagration and do not evaluate. xp hp 0, 3.3 Show the region.

A: To reverse the order of integration and do not evaluate.∫01∫x11y3+8 dy dx

Q: The curl of f(x,y,z)=xyzj is =.

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Q: a) Use Green's theorem to compute f F dr where c is a circle of radius R oriented CCW and F(x, y) =…

A: Green's theorem:∫C[Pdx+Qdy]=∫∫T∂Q∂x-∂P∂ydxdy where T is the region bounded by a simple closed curve…

Q: Use Stokes' Theorem to evaluate curlF · dS, where

A: Let, F→=xyz , xy , x2yz. Stokes theorem states that ," Where C is the boundary of surface oriented…

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: Evaluate ∫ ∫ √ (x2+ y2) dA where R is the portion of the annulus 1 ≤ x2 + y2 ≤ 16 with y ≤ 0 using…

A: We have to evaluate the double integral.

Q: Let Q be the rectangle formed by (0, 0, 0), (1, 0, 0), (0, 1, 1) and (1, 1, 1) oriented CCW as x² dx…

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Q: 1. Calculate y³ $ £ (-2² - sinz) dz + ( + v) ds. + dx dy, 3 3 where C is the circle of radius 1…

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Q: Find the area of the rigion lies between the circles r=2 and r=4cos(theta) in the first octant.

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Q: Ic F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + 5zj + 7yk,…

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Q: F(x, y, z) = yzi + 8xzj + exyk, C is the circle x² + y² = 1, z = 4.

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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: Let F = . Use Stokes' Theorem to evaluate curlF rlFds, where S S is the hemisphere x² + y² + z² = 4,…

A: I have explained everything with in the solution, please go through that.

Q: Let f(x,y) =sin(xy-x-3y+3) a) Find the domain and range of f b) Factor the argument on the sin…

A: Given .(a)As x and y can take any real values, the domain is R×R.The function f bounded between −1…