The following equation is an equation of a surface of revolution obtained by rotating a curve C (directive curve, radius function) in a coordinate plane, around a coordinate axis. Find an equation for C and identify the axis of revolution. x² + y² + z² = 1

Q: Find the exact arca of the surface obtained by rotating the curve: 3 24 = 5 sin Tr, 0 <I<1 about the…

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Q: 3. cos Tx – x*y + e*z + yz = 4 at point Po(0, 1, 2). -

A: The given surface at the point P0 is    Cos(pix) - x2y +exz + yz = 4

Q: Find an equation of the plane tangent to the following surface at the given points. zexy; (1,0,1)…

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Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x2 , (z =…

A: The distance of any points ( having same y co-ordinate ) on the curve is at same distance from…

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = √(9- [(x-1)] ^2)…

A: We need to find the equation of the surface. Please find step by step solution below:

Q: Find the ex9ct grea of the Surface obtained by revo lving the Curve f(x)=V5-x for x € (3,5] 9bout…

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Q: Find an equation of the tangent plane to the surface defined by the equation zf(x, y) + 2³ = 3 at…

A: The given surface is:zf(x, y)+z3=3The point is (-1, 2, 3)

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2)…

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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: Find the exact area of the surface obtained by rotating the curve about the x-axis. x3 y = 2 1 6x' 2

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Q: Find the equation of the surface of revolution generated by revolving the curve z²=4y in the…

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Q: find parametric equations for the given curve. y = x2, translated so that the minimum occurs at…

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Q: The area of the surface obtained by rotating the curve y = x2, 0 <x< 12 about the y-axis is

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Q: Find parametric equations for the surface obtained by rotating the curve y = 36x4 – x2, –6 <t< VI

A: Here we solve the given problem of calculus.

Q: 2. For the surface z = In(y+ Vx² + y²). (a) Find an equation of the tangent plane at the point (3,…

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Q: Consider the surface r²+y²+2ry-3x+2y-2z=1. Determine the following: (a) the general equation of the…

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Q: Find the equation of the tangent plane to x² the surface z = + y? 4 - at the point (2, 3, 10) x + 6y…

A: The equation of the tangent plane to a surface f(x,y,z) is given by:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. + 2)3/2, 3 sy s…

A: Given function is x=13y2+22 and 3≤y≤4 We have to find the exact area of the surface obtained by…

Q: Given the surface of revolution with equation y? = 3.x. 3 3 Find a generating curve of the surface…

A: Solution :-

Q: Write the equation for the surface generated by the revolving curve y = 2x +1, revolved around the x…

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Q: Identify a generating curve on the xz-plane for the surface of revolution with equation x2 + y? + 22…

A: Solution :-

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 4x2 - y2 +…

A: The equation of tangent plane to the surface z=f(x,y) at any point (a,b,c) is…

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x.(z 0)

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Q: x + y? – 4y + 2² = 0

A: Consider the provided question, Given equation of the surface, x+y2-4y+z2=0

Q: Find an equation of the plane tangent to the following surface at the given points. z =6 cos (x- y)+…

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Q: 3. (a) Find the equation of the plane tangent to the surface given by f(x, y) = 2xª+2y^+7xy at the…

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Q: Q3. Find the point(s) on the surface xyz 1 closest to the origin. %3D

A: Given: To find the points on the surface xyz=1 is given as,

Q: Find the equation of the tangent plane to the surface 9x +36y +4z? = 108 at the point (-2,1,-3).…

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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: Find an equation for the surface of revolution formed by revolving the curve z2 = 2y in the yz-plane…

A: To find the equation for the surface of revolution

Q: Find an equation for the surface of revolution formed by revolving the curve 2x + 3z = 1 in the…

A: Our Aim is to find an equation for the surface of revolution formed by revolving the curve 2x+3z=1…

Q: Find the equation of the surface of revolution formed by revolving the curve 2x + 3z = 1 in the…

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Q: 6. a. Find the length of the curve using the equation 12xy = 4x4 +3, from x = 1 to x = 3. b.…

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Q: Consider the surface defined by the equation z2 = 2x² + 4x - 6y? - 2y+ 1. %3D Find a set of…

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Q: Find the equation of the tangent plane to the surface x?+ Qy?-322=3' at (2-1,1) x²+ 2y 2-322=3'at…

A: Equation of a tangent plane

Q: Find the slopes of the surface in the x- and y-directions at the given point.

A: It is given that,z=xy  and point (1,2,2). We have to find the slopes of the surface in the x- and…

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: - - Consider the surface x² + y² + 2xy − 3x + 2y – 2z = 2. Determine the following: (a) the general…

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Q: Find parametric equations for the following curves in R³. (a) The great circle on the sphere x² + y²…

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Q: Find the equation of the tangent plane to the surface determined by a'y + z- 55 = 0 at a = 4, y = 3.…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 x = -(y2 +…

A: Given surface is x=13y2+232, 1≤y≤4, We know, If SA is the surface area of the curve by revolving…

Q: 4. Consider the equation 16y" - 4 + 2² = 16. By first deseribing all of its traces, sketch the…

A: Given,  The equation, 16y2 -4x2 + z2 = 16

Q: Given the surface of revolution with equation 22 y? 3x. 3 3 Find a generating curve of the surface…

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Q: 3. y = Vx,0< x<1 ; у-ахis

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Q: (y – 3)2 Consider the surface T with equation 4 + 22 = 1. %3D 3

A: We will identify standard  equation of type of quadratic surface by comparing   with given equation…

Q: Find the equation and sketch the graph of the surface generated by S revolved about the y-axis.

A: We are asked to find the equation of the surface generated by S revolved about the y-axis. The…