Find an equation for the surface of revolution formed by revolving the curve 2x + 3z = 1 in the xz-plane about the x-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: ind the equation for the tangent plane to the surface z = In(6x2 +9y2 + 1) at the point (0,0, 0).…

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

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Q: Find the points on the surface y2 36 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: The area of the surface obtained by rotating the curve y = 1sxse about the line x = 42 is

A: Given that y= 1/x  + x3 /12 and find the surface area. Here i attached solution of this question.

Q: Find an equation of the tangent plane to the surface given by z² – 2x2 – 2y? = 12 at the point (1,…

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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 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 an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^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: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y³ + z²…

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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: 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 section of the surface at y = 0. 9x^2+4z^2=36

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Q: Find an equation of the plane tangent to the surface

A: Given that : The equation is x2 + y 2 z 2 = 8 and the point P = ( 2, 2, 1).

Q: Find the point(s) on the surface xyz = 1 closest to the origin.

A: Given, g(x,y,z): xyz=1 distance from origin is  d=x2+y2+z2 f(x,y,z)=x2+y2+z2  square of distance…

Q: Find an equation of the surface of revolution obtained by revolving the plane curve 4x² – y² = 4…

A: The given equation of plane curve is 4x2-y2=4. Since the plane curve is rotated about x-axis,…

Q: Find the area of the surface generated by revolving the given curve about the x- axis: y = 19 – x²,…

A: Given,y=9-x2   squaring both the sides,y2=9-x2x2+y2=9x2+y2=32this is the equation of the circle with…

Q: Find the area of the surface obtained by rotating the parabola 1 y = 0 <x < 2, about the y-axis.

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

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Q: Find the equation of the surface of revolution of x = z2 about the x-axis.

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Q: Find the equation for the tangent plane to the surface z=-8x2 -4y2  at the point   (2,1,-36)

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Q: Find the area of the surface obtained by rotating the parabola 1 0 <x < 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 a² + y? + 2?…

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

Q: Find an equation of the tangent plane to the surface 2² + 2y? + z? = 175 at the point (5, -5, 10).

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Q: Find the equation for the tangent plane to the surface z=-8x2 -4y2 at the point (2,1,-30)

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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 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 when the curve y = x* 1 + ,on [1,2] is rotated 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: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: Find the area of the surface formed by rotating the curve with the equation x ^ (2) - (y ^ (2)) /…

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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: Find an equation of a generating curve given the equation of its surface of revolution. 8x2 + y2 +…

A: It is required to find the equation of generating curve given the equation of its surface of…

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

A: Solution-

Q: Find the equation for the tangent plane to the surface z= In (7x + 10y + 1) at the point (0,0,0).

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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 an equation for the plane tangent to the surface z = 2x2 - 7y at the point (3,-1,5)

A: Given surface z=2x2-7y and the point 3,-1,5. The main objective is to find an equation for the plane…

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 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: 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 the surface of revolution generated by rotating the part of the curve z= Sen…

A: Since there is no Sen function existed in math, the problem has been solved assuming the given curve…

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…

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.