find a parametrization of the surface. 1.The portion of the cylinder (x - 2)2 + z2 = 4 between the planes y = 0 and y = 3 2. Circular cylinder band The portion of the cylinder y2 + (z - 5)^2 = 25 between the planes x = 0 and x = 10

Q: State the type of the quadratic surface: x^2−(y/8)^2+z^2=1 1. Hyperboloid of two sheets 2.…

A: The given question can be solved as shown in step 2.

Q: 5. Find a parametric representation for the part of the sphere x + y + z2 = 4 that lies between the…

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Q: Consider the surface S which is the part of the paraboloid y = x ^2 + z^ 2 that lies inside the…

A: Given, the surface S: y=x2+z2 which lies inside the cylinder x2+z2=16.   a) Let x=vcosuz=vsinuThen…

Q: find a parametrization of the surface. 1.The surface cut from the parabolic cylinder y = x2 by the…

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Q: b) The curve y = }(r² – 2 In r), 1<r< 4, is rotated about the y-axis. Find the area of the resulting…

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Q: find a parametrization of the surface. The cap cut from the sphere x2 + y2 + z2 = 9 by the cone z =…

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Q: Find a parametric curve r(t) that represents the curve of intersections of the semi ellipsoid…

A: We will find the curve r(t) that represents the curve of intersections of two surfaces.Below find…

Q: find a parametrization of the surface Parabolic cylinder between planes The surface cut from…

A: To find a parametrization of the surface: Given that, Between the planes z=0 &amp; z=3 Thus, 0≤z≤3…

Q: Find the area of the surface. The part of the hyperbolic paraboloid  z = y2 − x2  that lies between…

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Q: Consider the surface given by x²z+ 2yz2 = 3æy?. %3D (a) Find and (b) Find the tangent plane to the…

A: Surface given, x2z+2yz2=3xy2 ....(i) a)we have to find ∂z∂x  and ∂z∂y  Take equation (i) and…

Q: 8.) Find a parametrization for the surface created by rotating the hyperbola z =-around the positive…

A: Consider the given information. Its purpose is parameterization for the surface by rotating the…

Q: Find parametrizations The portion of the hemisphere x2 + y2 + z2 = 10, y&gt;= 0, in the first octant

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Q: find a parametrization of the surface. The paraboloid z = x2 + y2, z&lt;=4 The paraboloid z = 9 - x2…

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Q: y A y=}x? 2

A: Please see the explanation below

Q: Find parametrizations The portion of the plane 4x + 2y + 4z = 12 that lies above the square 0&lt;=…

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Q: Find a point on the ellipsoid x² + 2y2 + z2 = 19 where the tangent plane is perpendicular to the…

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Q: Consider the ellipsoid 3x2+2y2+z2=18. Find all the points where the tangent plane to this ellipsoid…

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Q: Find a point on the ellipsoid x2 + 4y2 + z2 = 9where the tangent plane is perpendicular to the line…

A: To determine a point on the ellipsoid where the tangent plane is perpendicular to the line.

Q: find a parametrization of the surface Spherical cap The cap cut from the sphere x2 + y2 + z2 = 9by…

A: Given: Spherical cap The cap cut from the sphere x2 + y2 + z2 = 9by the cone z = √x2 + y2 To find a…

Q: Determine the area of the surface with parametric equat ions x = 2u?, y = v², z = 2uv, %D 0<u< 3, 0<…

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Q: z = x² – y? z = x² + xy – 1 and

A: Given - The intersection of the surface z = x2 - y2 and z = x2 + xy - 1 To find - The…

Q: 1. (a) Parametrize the curve of intersection of the sphere a? + y? + 22 22 + 222 = 1, Try your best…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the area of the surface. The surface in the first octant cut from the cylinder y = (2/3)z^(3/2)…

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Q: 3. Consider the curve y = x³, 0 < x < 3. (a) Find parametric equations for the surface obtained by…

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Q: dentify and sketch the section of the surface at y = 0. 4x² – y² + 4z? = 36 ype of the surface:…

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Q: 13. classify the surface: * 1 – y = 5x² + 6z² Elliptic paraboloid Cone O Sphere Plane O Ellipsoid

A: The given equation of the surface is: 1-y2=5x2+6z2

Q: 4. The surface described by the equation x2 + y + z² = 0 is a(an) (a) elliptic paraboloid symmetric…

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Q: 3. Find the exact area of the surface obtained by rotating the curve described by the parametric…

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Q: 10. Find a parameterization for the part of the plane x + 2y +z = 6 in the first octant. Compute the…

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Q: find a parametrization of the surface. 1.The upper portion cut from the sphere x2 + y2 + z2 = 8 by…

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Q: 1) Let S be the surface of the cylinder r+y = 4 with y >0 and -15z<1. Find a parametric equation…

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Q: parametrization of the surface z = 3x² + 8x, ymbolic notation and fractions where needed.

A: In this question, the concept of the tangent plane is applied. The equation of the tangent plane of…

Q: Find the area of the ellipse cut from the plane z= 8x by the cylinder x +y = 4. Surface area = (Type…

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Q: Tihe parameitric curve -1<I50 is rotated about x-axis. Find the surface area of the obtained solid.…

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Q: find a parametrization of the surface. (There aremany correct ways to do these, so your answers may…

A: Given information: The surface equation of the cylinder is y2+z2=9 between the plane is x=0 and x=3.…

Q: 3) Find the surface area of the portion of the paraboloid z = x2 + y2 below the plane z = 1. %3D

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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: Which of them are true? Ellipsoid II) y = 4z2 + 16z2 Hyperboloid III) Paraboloid z = 4 – 5y² – 9z²…

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Q: Find a parametrization of the ellipse centered at the origin in the xy-plane that has major diameter…

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Q: Find the area of the part of the surface ¤= (y/2 + z3/2) with y E [0, 2] and z E [0, 2]. Area =

A: For the solution of the problem follow the next step.

Q: Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x…

A: In the given question we have to find the double integral of paraboloid z=x2-y2 ovet the triangle…

Q: 17. classify the surface: 1 - y? = 5x² + 6z² %3D O Plane O Sphere O Elliptic paraboloid O Ellipsoid…

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Q: The surface x2 + y² = z² is identified as O A. Paraboloid O B. Cone O C. Hyperboloid of one sheet O…

A: the correct answer is option: D .) Hyperboloid of 2 sheets

Q: Find two parametric representations for the part of the ellipsoid 2x + y° + 22- 17 thất lieš tő thé…

A: Given:2x2+y2+2z2=17

Q: Q10. Consider the surface z = x²y + y - 2. At the point (2,1,3), find the following: 1) The equation…

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Q: Find the area of the surface obtained by rotating the curve of parametric equations: 6 x = 6t – t, y…

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Q: 10. Determine the characteristics of the equation 2 z = p' -q' and find the integral surface which…

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Q: 3. Parameterize the following surfaces: (a) The part of the elliptic paraboloid x+y^2+ 2z^2= 4 that…

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Q: Find a point on the ellipsoid x² + 4y² + z² = 30 where the tangent plane is perpendicular to the…

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Q: 4. Find the centroid of a thin flat plate covering the region enclosed by the parabolas y = 2r and y…

A: The given problem is to find the centroid of the thin flat plate covering the region enclosed by…