Find the points on the surface y? = 81+ xz that are closest to the origin.

Q: Find the surface area of the object obtained by rotating y = 1 +. 8x2 , 2<x 3 about the x-axis. 4

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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 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: (b) Sketch the trace of the surface z = 2x? – y? when x = -1. Label your axes, and give the…

A: Given surface is  z=2x2-y2          (i) By putting x=-1 in (i), the surface becomes z=2-y2 The graph…

Q: Identify and sketch the graph of the following SURFACES. x² + y² = sin²z, z = [0, π]

A: Any point on the 3D plane is represented using the ordered pair: x, y, z. A graphing utility can be…

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 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: The area of the surface generated by revolving the curve y = V9 - x,-2 s xS 2 about the x-axis is…

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

A: Given  y =x3 ,  0 ≤ x ≤2The area under a curve is the area between a curve f(x)and the x-axis on an…

Q: Find the point on the surface z = xy + 1 nearest the origin.

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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: Use traces to sketch and identify the following surface 25x² + 4y? + z² 100.

A: Given: The surface 25x2+4y2+z2=100.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V6 - x, 4 <…

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

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Q: for y^2 - z^2 =1, find the point(s) on surface nearest to origin

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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 the area of the surface obtained by revolving the graph of y = √x(4x − 3)/6, 1 ≤ x ≤ 9 about…

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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 exact area of the surface obtained by rotating the curve about the y- axis: y = 3 + 5x?,…

A: Consider the given function and interval. y=3+5x2, 3≤x≤8 If y=f(x) is function and the interval of y…

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 area of the surface generated by revolving the curve, x = /6y – y? ; 2sys 5

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

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

A: Given the equation4x2+9z2=36

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

A: To find the surface area of the object obtained by rotating y=x36+12x ,  1≤x≤2 about x-axis.  Let,…

Q: What is the name of the surface defined by the equation -y? + x? = 1?

A: We have to find surface name defined by the equation -y2-z22+x2=1

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

A: Solution :-

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: Sketch the section of the surface at y=0. z = /2+x² + y?

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Q: The area of the surface obtained by rotating the curve y = v64-x2, -2 <x < 2 about the x-axis is

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Q: sketch the given surface. y 2+ z 2 = 1

A: To sketch: The surface y2+ z2 =1 Concept used: The general equation of the cylinder whose base…

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

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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 surface in R' of the equation presented. x2 + y? - 8x = 0

A: Sketch the graph on xy-plane, i.e., when z=0

Q: Describe the surface given by the equation, and find xy-trace, xz- trace, and yz-trace. 16x2 + 16y?…

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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: Find the area of the surface generated when y² = 12x is revolved about the x- axis from x = 0 to x =…

A: Given curve,y2 = 12xRevolved about x-axis from x=0 to x=3.

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 area of the surface obtained by rotating the circle x^2+y^2=r^2 about the line y=2r

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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: (a) Find the area of the surface generated by the given curve about x-axis y = Vx , 18 x< 4

A: Note: According to Bartleby guidelines; for more than one question asked only the first one is to be…

Q: Find the point on the surface r² – 2ry + 2y² – x +y = 0 closest to the point (1, 2, –3).

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Q: Sketch the section of the surface at y = 0. z = V4 +x² + y? 6 6 -8 -6 -4 -2 -2 -5-4-3--1, -8 -6 -4…

A: Given query is to the graph of the given expression.

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 area of the surface generated by revolving about the x-axis the upper half of the ellipse…

A: IN THIS QUESTION WE HAVE TO FIND AREA FROM REVOLUTION OF A ELLIPSE.

Q: Find the area of the surface obtained by rotating the curve y2 = 4x + 4 0<x<8 about the x-axis? %3D

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Q: The area of the surface generated by revolving the curve y = y9 - x2,-2 < x < 2 about the x-axis is…

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Q: Find the points on the surface 2 2 xY + 100 that are closest to the origin.

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Q: Find the area of the surface obtained by rotating the curve y² = 4x + 4 0<x<8 about the x-axis?

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