х3 , у-4 — 2г, 0 sts2 (а) х-ахis (b) у-аxis

Q: Find the area of the surface generated by revolving the curve = V¤ + 3, 4 < y <7

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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 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 of the tangent plane to the surface z = 5y – 4x? at the point (-4, 2, -44).

A: The solution is given as

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: Which of the following is the surface area of the solid body created by rotating the given…

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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: A particle follows the trajectory x(t) = t3 + 2t, y(t) = 20t – t2 with t measured in seconds and…

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Q: The surface of a mountain is modeled by the equation h(x, y) = 5000 − 0.001x2 − 0.004y2. A mountain…

A: Hints:  The given equation is h(x,y)=5000-0.001x2-0.004y2 and the given point is (500,500,3750). To…

Q: Find an equation of the tangent plane to the surface at the given point. - 2xy + y², (3, 5, 4) eBook…

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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: Find the equation for the tangent plane to the surface at the indicated point. -4x – y+ 2z = 1, P(1,…

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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: The surface of a mountain is modeled by the equation h(x, y) = 7000 - 0.001x2 - 0.004y2. A mountain…

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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: Determine the surface area generated by revolving the line segments about y-axis. 3m 4m 2m 1m 2m 2m…

A: Given , Line segment revolve around y-axis , we have to find surface area of formed shape .

Q: Find the area of the surface generated by revolving the curve about each given axis. x= 5t, y- 9t,…

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Q: Find an equation of the plane tangent to the following surface at the given point. z = 6 - 4x2 - y2;…

A: By using equation of tangent plane for surface, we calculate the required tangent plane.

Q: Sketch the section of the surface at y= 0. 4. + 9 36

A: Given the equation4x2+9z2=36

Q: Find the area of the surface generated by revolving the curve about each given axis. x St, y 2t, 0st…

A: Given that        x = 5t , y = 2t  , 0 &lt;= t &lt;= 5  Here we have to find the area of the surface…

Q: Find an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

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Q: Find the length of the parametric y = 2 , - V3sts V3. curve x = 1+

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Q: . Find a parametrization for the circle (x – 2)² + y² = 1 starting at (1, 0) and moving clockwise…

A: Consider the equation of circle

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 cylinder surface determined by Curve 4x?+9g? -36=0 and d= ( 1, -1. 32 line.

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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: 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: Find an equation of the plane tangent to the following surface at the given point. z= 3- 3x -y:…

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Q: Consider the curve C which is the intersection of the surfaces shown in the attached figure.

A: To evaluate the below integral. ∫Cx−y−2zds

Q: Find the area of the surface generated by revolving the curve about each given axis. X = 4t, y = 8t,…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 4t, y = 7t,…

A: x=4t y=7t

Q: Find an equation of the tangent plane to the given surface at the specified poin 8x2 + y2 - 7y, (1,…

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

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Q: Find the equation of the tangent plane at the point (-2,1 – 3) to the ellipsoid surface + y? + = 3.

A: Find the equations of the tangent plane and normal line at the point (-2, 1, -3) to the ellipsoid…

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 an equation of the tangent plane to the given surface at the specified point. z = 6x² + y² -…

A: This question is based on finding equation of plane to the given surface at a point.

Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2, - 5) and…

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Q: Which of the following best describes the surface represented by the equation -- =1? cylindrical…

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Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

Q: Example: Find the surface area of the curve described by x = t³, y = t², 0<t<1, rotated about the…

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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…

Q: Find the length of the curve given by the parametric equations z = 2t3/2 0 <t< 4 ' y = 3t + 1

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