Sketch the surface in R' of the equation presented. 4x² + y? = 36 Interactive 3D Graph - 10 Interactive 3D Graph O Help Interactive 3D Graph O Help Interactive 3D Graph O Help 10 10

Q: Find an equation of the surface of revolution generated by revolving the plane curve about the…

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Q: Find an equation for the surface of revolution formed by revolving the curve in the indicated…

A: Given equation of curve is z = ln x The radius function about z axes is  r(z) = x = ez

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 for the surface consisting of all points P for which the distance from P to the…

A: Let, P(x, y, z) be the point on required surface.

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation.…

A: Given rectangular equation is y = x2

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation…

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Q: Find the area of surface that is generated by revolving the portion of the curve 9 – y² , – 2 < y< 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 surface generated by revolving the curve y = 1/x about the x-axis.

A: When y = f(x) is rotated about x axis, we get a surface with parametric representation is,…

Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x², 0sis…

A: y=1-x2,  0≤x≤12 Differentiating with respect to x, we get dydx=121-x2·0-2x=-x1-x2

Q: Sketch the surface with equation x^2 + y^2 + 2z^2 − 1 = 0.

A: The given equation is x2+y2+2z2-1=0

Q: 21 y2 a. x + 1 %3D

A: The given equation is x21+y29+z24=1We know the general equation of ellipsoid is x2a2+y2b2+z2c2=1So…

Q: Find an equation which describes the surface created by rotating (r, x, 0) around the r-axis. Note…

A: Our Aim is to find an equation which describes the surface created byrotating (x,x,0) around the…

Q: Find the equation of the surface of revolution that is generated by rotating the straight line y = x…

A: The surface of revolution that is generated by rotating x=f(y) around the y-axis is x2+z2=f(y)2 so…

Q: Given a surface, ƒ(x,y,z)=15, explain what you would do to find the equation of the tangent plane at…

A: Nothing

Q: Find the exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1/3 ( y2…

A: Given curve is x=13y2+232 over 1 ≤ y ≤ 2. The exact area of the surface obtained by rotating the…

Q: Find an equation of the surface obtained by rotating the curve y = 1- sqrt(z) (square root of z)…

A: Given the equation of curve, y=1-z This can be written as z=1-y On squaring both sides, z=(1-y)2…

Q: Find

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Q: Identify the type of surface represented by the given equation. x= - 72?, no limit on y O Cylinder O…

A: Consider the given equation, x=-7z2 This equation is of the form of parabola on the xz-axis and y…

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

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Q: Write the equation for the surface generated by revolving the curve x2 - 2y2 = 1 about the y-axis.…

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Q: The parametric curve x=2sin(t)+2, y=3cos(t)-2 describes a clockwise traveling  vertical ellipse with…

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

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3,    0 ≤…

A: We have to find the area of surface.

Q: Identify a generating curve on the xz-plane for the surface of revolution with equation a² + y? + 2?…

A: Consider the surface of revolution with equation, x2+y2+z2=e2x it is required to find the generating…

Q: Which one, y=ex, 1≤y≤2, gives the surface area of the solid formed by rotating the curve segment…

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Q: Find an equation for the surface of revolution formed by revolving the curve in the indicated…

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Q: Find an equation of the surface of revolution generated by revolving the plane curve about the…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1/3(y2 +…

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Q: Find the surface area generated by rotating the first quadrant portion of the curve  x2=16-8y about…

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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: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1/3(y2 +…

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Q: The surface defined by the equation z= 4x2 + y2 is called an elliptical paraboloid. a. Write the…

A: Given, function

Q: The curve y= 7,0 <x <3; is rotated about the x-axis. Find the exact area of the 3 resulting surface.

A: Given: The curve is Interval is from 0  to 3  and it is rotated about x axis

Q: find an equation for the surface generated by revolving the curve about y-axis. y = 4x2, (z = 0)

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Sketch the graph of the equation in xyz coordinate system and identify the surface 8x? + 4y? – z2 =…

A: Sketch the graph for the given surface.

Q: Consider the surface given by the equation 22 – 5y? + 2? + yz = 32 (a) Find the equation of the…

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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: Describe and sketch the surface y2 + z = 6

A: Graph: Given surface y2+z=6 Since one co-ordinate has power 2 and other co-ordinate has power 1. So…

Q: Let S be the surface with equation 4y2 + 4z2 - x2 - 16 = 0 1) Find an equation of a generating…

A: The given equation of surface is 4y2+4z2-x2-16=0 To find a generating curve of revolution.

Q: The 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotationing it out of the xy-plane and…

A: To answer it, let us go through the equation of Hyperboloid of 2 sheets   x2a2 - y2b2  - z2c2 = 1…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.

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Q: 5. y-z =16

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.  x=1/3(y2 + 2)…

A: The given curve is,

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. (y2 + 2)3/2, 2 <…

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Q: Consider the equation of the surface S given by -3x - 2y³z4+ xy = -4 where a and Bare pair numbers,…

A: Use formula of equation of Tangent plane