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

Q: Find the area of the surface generated when the curve y [2,4] is rotated about the y-axis.

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Q: Graph the curve 8y2 = x2 (1 − x2 ). Use a computer algebra system to find the surface area of the…

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Q: Find the area of the surface generated by revolving the parametric curve x = t, y = 2t² (0 ≤ t ≤ 1)…

A: Given, x=t,y=t2,0≤t≤1 The area of the surface generated by revolving the parametric curve about the…

Q: Find the area of the surface generated by revolving the curve about the (a) x-axis and (b) y-axis.…

A: Explanation and solution is given below....

Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x, 0 <xs;…

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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 an equation for the surface obtained by rotating the line z = 7y about the z-axis.

A: We need to determine the equation of the surface that is obtained by rotating the line z=7y about…

Q: z = In (x² + y²) at point Po(1,0, 0).

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Q: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y³ + z²…

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Q: The area of the surface obtained by rotating the curve y = x2, 0sxs1 about the y-axis is

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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: Find the area of the surface obtained by rotating the curve x = /16 – y², 0 <y<2, about the y- axis.…

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

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

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Q: Find

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Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + z?…

A: Given: Surface of revolution with the equation x2+y2+z2=e2x To find: Identify a generating curve on…

Q: Find the exact area of the surface obtained by rotating the curve x = (1/3)y^3, 0 &lt;= y &lt;= 1,…

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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 the area of the surface generated by revolving the curve y = √(x2 + 2), 0 ≤x ≤ √2, about the…

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Q: The area of the surface obtained by rotating the curve y = 25-x² , -4 sx<4 about the x-axis is

A: Area of the surface rotated about x -axis is, a≤x≤b,…

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 the area of the surface generated by revolving the curve y=−x^3/18​, −2√2≤x≤0​, about the​…

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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: (d) Find the area of the surface generated by revolving the curve y = 2a, 0 < x < 3, about the…

A: Part (D) To find the area of the surface generated by revolving the curve, y=2x,0≤x≤3, about the…

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: Let C be the curve y =x3/2, 1 < x < 4. (a) Find the length of this curve. (b) Find the surface area…

A: Given curve is

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 11x ,(z = 0)…

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Q: 4. Find the area of surface that is generated by revolving the portion of the curve I = 2/1- y,…

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

A: Find the exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1+ 2y2 ,1…

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + Z?…

A: Solution-

Q: Find the exact area of the surface obtained by rotating the curve x = 1/3y3, 0 &lt;= y &lt;= 1,…

A: For rotation about y-axis, the surface area of the curve is given by

Q: Find the area of the surface generated by revolving the curve y=- 24 .Osxs/6. about the x-axis.

A: area = ∫06 ydx area = ∫06  x3dx/24 area = [x4/96]60 area = 6*6/96 - 0 area = 3/8

Q: Provide a parameterization for the surface formed by revolving the curve y=VX around the X-axis, for…

A: To Determine :-  Provide a parameterization for the surface formed by revolving the curve y = x…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 5 + 4y2,…

A: We use the formula S=2π integration of y √(1+x'2)dy from 1 to 2

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: Find a set of parametric equalions for the surface formed when the curve y(1+z²) – 1 = 0 is revolved…

A: Find a set of parametric equations for the surface formed if the curve y1+z2-1=0 is revolved about…

Q: Find an equation of the plane tangent to the surface z2 - xy = 14 at (2, 1, 4).

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

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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: Find the area of the surface obtained by rotating the curve y=1/3 x3/2, 0≤y≤12  about the y- axis.

A: Let a rectangular strip parallel to x-axis of thickness dy be made whose tip touches the curve…

Q: Find the area of the surface resulting from rotating the curve: x=5t−1, y=2t^3, -2≤t≤1, around the…

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Q: Give an equation of the surface of revolution generated by revolving x In z about the z-axis.

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Q: Find the equation of tangent plane to the surface x? + 2y? + 3z2 = 21 which is parallel to the plane…

A: equation of the tangent surface of  F= x2+ 2y2+ 3z2= 21   which is also parallel to the plane…

Q: Find the surface of revolution of the curve y = 4 + 3x² that is rotated about the y- axis between 1…

A: We have to find the area of the surface of revolution of the curve y=4+3x2 that is rotated about the…

Q: Find the area of the surface generated by revolving the parametric curve x = t², y = 2t (0 ≤ t ≤ 4)…

A: A detailed solution is given below.

Q: Find the exact area of the surface generated by revolving the curve about the stated axis. y = Vx…

A: The formula for area of surface generated by the revolution of curve y=f(x) , a≤x≤b about x-axis.…

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 6t, y = 9t,…

A: Here,  we need to find the surface generated by revolving the curve x=6t, y=9t, 0≤t≤3, about each…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.