Find the area of the following surface using a parametric description of the surface.   The cap of the sphere x2 +y2+z2=25 for 2≤z≤5

Q: Calculate the surface area of the following: the cap cut from the sphere r² + y² + z² = 3 by the…

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Q: (c) The cone r² = 4(y² + z?) for (0 <x < 4

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Q: Find the following: The traces of the surface x2 + y? + 22 = 6 in the planes parallel to the…

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Q: The distance between the centers-of the following two spheres: x²-22x+y2-58y+z?=-961,…

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Q: Determine the points on the surface y2+z2−x=8 that are closer to the origin.

A: Consider the given surface. y2+z2−x=8z2=8−y2+xf(x,y)=8−y2+x

Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

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Q: Consider the surface given by the equation z – y = x². Draw a total of at least 3 traces in at least…

A: It can be solved in 2nd part using simple geometry.

Q: Which of the following quadratic surfaces describe an elliptic paraboloid shape ? OA. z = 2? – y² +…

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Q: Evaluate yds where S is the surface = x + 2y?, 0 <a < 1, 0<y S 2

A: Consider the surface, z = x + 2y²

Q: a. Which of the following surface graphs represents f(x,y) = y²? OA.

A: Given, the surface                           z=f(x, y)=y2

Q: cribe the surface with equation x + y° + z? + 8x + 4y + 2z – 43 = 0 surface is a sphere with center…

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Q: Which of the following surfaces could have contour map 5 2 1 1. cone 2. parabolic cylinder 3.…

A: Please see the below picture for detailed solution.

Q: sketch the given surface. x2 − 4y2 = z

A: Given: x2-4y2=z Divide the equation both sides by 4. x24-4y24=z4x222-y21=z4 The equation…

Q: w.The given.surface.at. thespeeif 2.

A: Introduction:   We know that the equation of tangent plane to the surface z=f(x,y) at the point…

Q: Consider the surface shown in the following figure: If h, k, r, m, teR. A general equation that…

A: Solution is below

Q: Which one of the following surfaces is the aph of f(z, y) = y -2 ? 3..

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Q: If the infinite curve y = e-6x, x > 0, is rotated about the x-axis, find the area of the resulting…

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Q: 1. Find the area of the part of the surface z = a? + 2y that lies above the triangle with vertices…

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Q: Find the surface area of the plane ( 15x- ? 5z+20y=D35) if it is in the first octant

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Q: Find the points on the surface z2 = xy + 4 closest to the origin.

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Q: sketch the given surface. x = 1 + y 2+ z2

A: sketch the given surface. x = 1 + y 2+ z2

Q: Find the area of the surface generated by revolving the curve, x = /6y – y? ; 2sys 5

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Consider the portion of the plane x + 2y + 3z = 12 that sits above the circle (x − 2)^2 + (y − 2)^2…

A: The solution are next step

Q: If the infinite curve  y = e−4x, x ≥ 0,  is rotated about the x-axis, find the area of the…

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Q: If the curve y = f(x), a ≤ x ≤ b, is rotated about the horizontal line y = c, where f(x) ≤ c, find a…

A: Given, Curve y= f(x) , a≤x≤b Rotated about a horizontal line y=cwheref(x)≤c

Q: If the maximum distance from the surface x? + 2y² + z? = 3 to the point (1,0, –1) is Va+ bv6, what…

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Q: The solid that is the common interior below the sphere x + y + z = 80 and above the paraboloid z =…

A: We need to find the upper limit for the given integral.region is bounded below by the sphere and…

Q: Identify the surface in the xyz coordinate system given by the equation: z=-√(4-y^2) O cylinder O…

A: Let's find.

Q: Let (P) be the surface given by the following equation z = 5-x²-y² and (Q) be the surface given by…

A: Given surface P is, z=5-x2-y2    ----(1) For xy projection, put z=0 in (1) we get, 0=5-x2-y2⇒…

Q: Sketch the portion of the surface that lies in the first octant: y= z.

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Q: Sketch the surface r = 2y? + 32².

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Q: Evaluate F dS, S where 4 F(x, y, z) = (3y, -2x, -), and S is the surface that is composed of the…

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Q: Explain why C lies on the surface of the cylinder x² + y² = 1.

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Q: sketch the given surface. y 2+ z 2 = 1

A: To sketch: The surface y2+ z2 =1 Concept used: The general equation of the cylinder whose base…

Q: If the infinite curve y = e-2x, x 2 0, is rotated about the x-axis, find the area of the resulting…

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Q: If the infinite curve  y = e−8x, x ≥ 0,  is rotated about the x-axis, find the area of the…

A: Given: y=e-8x , x≥0

Q: 7. Use a program to plot the surface generated by the following equation: 4x – 16y + z? = 16

A: we need to plot the following surface generated by, 4x2-16y2+z2=16

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

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Q: Find the area of the cap of the sphere x2 + y² + z? = 2 cut by the cone z = Vx2 + y² |3D

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Q: Which of the following is a non-orientable surface? O a. all the other choices are orientable O b.…

A: orientable surface -  The surface for which we can define clockwise consistently.

Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

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Q: 3. Use traces to sketch and identify the following surface 25x2 + 4y² + z2 = 100.

A: Consider the given: Given:25x2+4y2+z2=100Let x=k∴25x2+4y2+z2=100             4y2+z2=100−25x2Hence,…

Q: What are the reace curves of this surface for x=0, y=0, and for z=k? Name the shape of the surface.…

A: Note : In the question it has to be '' trace curves '' instead of '' reace curves ''. So, we are…

Q: Which surface has the following equation? x2 – 2y = 32 O Cylinder O Plane Paraboloid Hynerboloid

A: Please refer to the image below

Q: Determine the sections of the following surface on planes parallel to the xz plane. -y+ = 1 %3D O…

A: here first we solve for the surface and then check it .

Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…

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Q: Find the exact area of the surface obtained by rotating the curve abo = V7 - x, 1<x< 7

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Q: Use traces to sketch and identify the following surface 25x2+4y2+z2=100

A: Ellipse is a closed curve around 2 focal points such that for every point on that curve, the sum of…