If F(x, y, z) = xzi+3ryj-2zk, evaluate fF.dS using Gauss's theorem when S is the closed cylinder bounded by the surface x² + y² = 1 and the planes z = 0 and 2 = 3.

Q: Assume S is the surface x1000 + y8000 + z1000 = 1,000,000 and F = [9 + ee^(xyz), x8yz, 3x - 5y -…

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Q: = 21 which is parallel to the plane Find the equation of tangent plane to the surface x? + 2y? + 3z2…

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Q: Consider the function f(x, y) = (e - 3x) cos(y). Suppose S is the surface z = f(x, y). (a) Find a…

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Q: An equation for the tangent plane to the surface : = (xty at the point P(1, 1, 4) is a) 8x + 8y -: =…

A: Equation of a tangent to the surface z=f(x,y) at point (a,b,f(a,b)) is given by…

Q: Suppose given a function f(x, y, 2) of three variables, and a point (o, y0, 20) €R. Explain in your…

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Q: If Φ = xy^2 + 6 z^3 x^2, find  ∇Φ and |∇Φ| at the point (6,2,2)​ ​

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Q: The horizontal tangent plane of the surface z = 4x – xy – 2y – 2x – 8y – 3 is given by the equation…

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Q: A surface has Cartesian equation :- f(xy). given by f(1.9)=6xy-5x -3y+ +7x-6y a) Use any…

A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

Q: H. Use the gradient to find the equation of the tangent plane to each of the surfaces at the given…

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Q: Suppose F(x,y)=. Use Green's Theorem to calculate the circulation of F around the perimeter of the…

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Q: An equation for the tangent plane to the surface (xty at the point P(1, 1, 4) is a) 8r + 8y-:= 0 b)…

A: The given surface is  f(x,y)=z=(x2+y2)2  ...........(1); we have to find the tangent plane at point…

Q: Consider the surface S of equation 2 = x² + y*" An equation for the tangent line tangent to S at…

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Q: The roof of the Monterrey Campus gymnasium has the shape of the hyperbolic paraboloid given by the…

A: Here we have to use directional derivative  Directional derivative of a function f(x,y,z) in the…

Q: The tangent plane to the surface 2x² + 3y² = 5z² at (1, 1, 1) has an equation ax +by+cz = d.What is…

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Q: The equation for a plane tangent to z = f(x, y) at a point (xo, Yo) is given by z = f(xo, Yo) +…

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Q: a) Letfx, y) = xe-y+ 5y.Find the slope of the surface z = fx, y) in the y-direction at the point (3,…

A: NOTE: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the equation of the tangent plane to the surface of the equation z = x2 + y2 - 2xy on the point…

A: Equation of tangent plane

Q: Find the extreme values of the function f(x, y, z) = xy + z^2 on the circle in which the plane y - x…

A: Given function is fx,y,z=xy+z2. We have to find the extreme values of the given function on the…