Let S be the closed surface given by 2¹+ y² + 24 = 1. (For a figure for such a surface, see the lecture notes for this section) Evaluate (V x F)-n do, where F = (2xy² cos z, x+yze, zyz) and n is the outer normal.

Q: Which of the following lines is parallel to the normal line of the 2x²y + yz - xz = 1 surface at the…

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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: A surface z = f(x, y) is defined implicitly by the equation x +y+ z – e² = 3 – e. - Determine the…

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Q: 8. Find a normal for the plane that passes through the points: P(2,-2, 3), Q (3, 2, 1), R(-1,-4, 2)

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Q: Let S be the portion of the plane 2x + 3y + z = 2 lying between the points (-1, 1, 1), (2, 1, −5),…

A: S is the portion of the plane 2x+3y+z=2 lying between the points (-1, 1, 1), (2, 1,-5), (2, 3,-11)…

Q: 2. -) Consider the surface x² + y²-2xy-x+3y-z=-4 at the point Po(2, -3, 18). Determine the…

A: Let's find equation of tangent plane and parametric equations of normal line.

Q: Suppose that the plane tangent to the surface z = f(x, y) at (2, 7, 8) has equation z + 8x – 2y =…

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Q: ) Consider the surface x² + y²-2xy-x+3y-z=-4 at the point Po(2, -3, 18). Determine the following:…

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Q: < 2x and –1 < u < 11. your solution using the form (*,*,*). Use symbolic notation and

A: Introduction: Surfaces in R3 have two degrees of freedom; it is possible to vary two parameters…

Q: #10 For the surface x³-2xz+y4+1=xy do: (a) Find the tangent plane at point (1,1,1),, Find…

A: (a) Equation of tangent plane at point (1,1,1) is: y=1(b) Equation of normal line at the point…

Q: Consider the surface given by x2 + y? + z? = a². Show that every normal line to this surface passes…

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Q: 4) The curve y = x²,-1<x< 0 is rotated about the y -axis. Find the surface area of the resulting…

A: The formula for calculating the surface area (say S) of the curve y=f(x) is given by:…

Q: Use the computer to plot the surface x+ y +z = 1. What type of surface is this? Print your result…

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Q: 3. Find the points on the surface z = = xy + 2 that are closest to the origin.

A: Let g(x,y,z) be the constraint function and f(x,y,z) be the function whose extreme values to…

Q: Use hyperbolic functions to parametrize the intersection of the surfaces x² - y² = 25 and z = 5xy.…

A: Here we have to parametrize the surface using hyperbolic functions.