Consider the surface S with equation 4 x² - y² = 1. Identify the type of quadric surface that S is and give a rough sketch of it (Label some points so that we can understand the scale of your sketch Find all points P on S where the tangent plane to S at P is parallel to the plane x + y + 3z = 2022. Let S be the part of S with 2 ≤ z ≤ 4. Evaluate the surface integra JJ₂√₁- x² - y² do. Š

Q: The surface described by the conditions 2 + y? + z² = 4, x 0 is the same as the surface described…

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Q: sider the surface z = f(z, y)=√√/25 - 1² - y².

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Q: 2. Consider the surface defined by 1² + 2xy + y² + 2²-25 Let F(x, y, z)-1² + 2xy + y² + 2². (a)…

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Q: Identify the quadric surface with equation -a + 9y? – z = 0. O elliptic paraboloid O hyperbolic…

A: given  -x2+9y2-z=0

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: (2u cos v, 3u sin v, u²) and find tangent plane at Describe/Sketch the surface given by r = (0,6,4)

A: Given, To find: equation of tangent plane ate (0,6,4)

Q: Identify the surface whose equation isľ = 3 sec (0). O Circle O Hyperbolic Paraboloid O Cone Sphere…

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Q: 1. Find the elements of surface area dS and dS, in terms of du and dv, for the surface S given…

A: Vector calculus

Q: Consider the surface given by z = 4x² + y². Draw the level curves for this surface in the (ry) plane…

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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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