Find the point(s) on the surface z2 = xy+1 which are closest to the point (10, 8, 0). List points as a comma-separated list, (e.g., (1,1,-1), (2, 0, -1), (2,0, 3)).

Q: Sketch the section of the surface at y = 0. 2x + z = 3 4 -8 -6 -4 2/4 -2 6 8 -6 -8- 6. AM -8 -6 -4-…

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Q: Sketch the surface.......... ASSORTED ............... 4y2 + z2 - 4x2 = 4

A: Given :             The given function is 4y2 + z2 - 4x2 = 4 And can be written as,…

Q: Find the surface area for the portion of the surface f(x,y)=1-x² + y that lies above the triangular…

A: Solution :

Q: Consider the surface z = (x+ 1)² + (y – 2)² – 1 Does the point (1, 3, 1) belong to this surface?

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Q: Find the points on the surface x2 - zy = 4 closest to the origin.

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Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

Q: A 2-D surface was found in one research group of scientists and a surface equation has been derived…

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Q: Determine the projection of the following surface on the xy plane. (xy trace) 4z-목 + =0

A: here first solve the given surface and then we trace it

Q: Find the area of the surface.The part of the surface 2y + 4z − x2 = 5 that lies above the triangle…

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Q: FIND THE AREA OF THE SURFACE FOR THE PORTION OF THE PARABOLOID Z = 49-x² - y² IN THE FIRST OCTANT

A: Formula: The surface area of the function z=fx, y over the region D is: SA=∫∫D1+zx2+zy2 dA The given…

Q: Sketch and identify the surface given by x2 + 4y + 4z2 = 0.

A: Equation of the surface is given by:x2+4y+4z2=0 we need to identity the surface and hence sketch the…

Q: sketch the given surface. x2 − 4y2 = z

A: Given: x2-4y2=z Divide the equation both sides by 4. x24-4y24=z4x222-y21=z4 The equation…

Q: Classify the surface: 1 – x = 3y + 4z?

A: Given :  The surface 1 - x = 3y2 + 4z2.   To classify the given surface.

Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (2, 2, 0).

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Q: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

Q: Find an equation of the surface consisting of all points P(x, y, z) that are twice as far from the…

A: Let d1 be the distance from the point 0,0,1 to the point Px,y,z and d2 be the distance from the…

Q: sketch the given surface. x = 1 + y 2+ z2

A: sketch the given surface. x = 1 + y 2+ z2

Q: Determine the area of the surface. The part of the surface z=1+3x+2y^2 lying on the triangle with…

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Q: Find the area of the surface. The part of the surface 2y + 4z - x2 = 5 that lies above the triangle…

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Q: Describe and sketch the surface x2 + z2 = 4

A: Given- x2+z2=4 To sketch- The graph of the above function and explain it.. Concept Used- The…

Q: Use traces to sketch and identify the surface -x2+ 4y2-z2=4

A: To identify the surface, set each variable to some constant and find what type of surface produces…

Q: Find an equation of the surface consisting of all points P(r, y, z) that are twice as far from the…

A: To find an equation of the surface whose all points are twice as far from the plane z=-4 as from the…

Q: Find a generating curve and the axis of revolution for the surface                             x2 +…

A: Find a generating curve and the axis of revolution for the surface   x2+3y2+z2 =9 If the equation of…

Q: the trace of the surface in the plane x=1?

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Q: 4. Find the area of the surface S where S is the part of the plane z = 3x +y that lies above the…

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Q: Sketch the surfaces HYPERBOLOIDS (y2/4) - (x2/4) - z2 = 1

A: we have to sketch the surface of the hyperboloids  y24-x24-z2=1

Q: Find the maximum and minimum values of a function F(x,y.z)3D8X+y+ z on the surface A

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Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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Q: The portion of the surface z = 2x + y2 that is above the triangular region with vertices (0, 0), (0,…

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Q: Evaluate the surface z =1,0<x,y <1.

A: To solve this we will use divergence theorem.

Q: Find the slope of the surface z = f (x, y) in the y-direction at the point (64, 8).

A: Follow the procedure given below.

Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

A: According to the given information, it is required to find the area of the surface.

Q: Find all points on the surface xy - z2 = 1 which are closest to that origin. Let x,y,z be the…

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Q: Find the area of the surface. The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

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Q: Given the surface of z =10-4x² – y² : Sketch the surface of z=10-4x² – y² where z>0 and show the…

A: Given:-               z = 10- 4x2 - y2z = 10-- 4x2 + y2

Q: Classify the quadric surface ² - y² - x² + 4x = 5. 2 य

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Q: The part of the surface z =1  + 3x+ 2y 2 that lies above the triangle with vertices (0, 0), (0, 1)…

A: Part of the surface: z=1+3x+2y2∂z∂x=3, ∂z∂y=4yVertices of the triangles are (0,0) , (0,1) , (2,1)

Q: Find the points on the cone z = x° + y° that are closest to the point (1,-1,0) %3D +1

A: Given,

Q: Sketch the surface 1<z</9-x² - y² and x²+y² <1

A: To sketch the given surfaces.

Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y° and z = 25 – x² – y² .

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Q: Find an equation of the sphere containing all surface points P = (x, y, z)  such that the distance…

A: Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance…

Q: (a) Find max, min or saddle points for the surface Z= x* - 3xy + 5x

A: We have to find first and second order partial derivatives.

Q: 6. The part of the surface z = 1 + 3x + 2y² that lies above the triangle with vertices (0, 0), (0,…

A: Given: A surface z=1+3x+2y2 and vertices of triangle (0, 0), (0, 1) and (2, 1). To find: Area of…

Q: A trace of the surface +- z = 0 on the xy- plane is: O Point at (3, 2, 0) O Circle Ellipse Point at…

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

Q: Q1/ Use traces to sketch and identify the surface z2 - 4x2 - y² = 4

A: Let's find.

Q: Find the area of the surfaces The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

A: The surface cut from the '' nose '' of the paraboloid x=1-y2-z2 by the yz plane .…

Q: The part of the surface z-1+ 3x + 2y that lies above the triangle with vertices (0, 0), (0, 1). and…

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Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

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Q: 2) Find the area of the part of the surface z = x2 + 2y that lies above the triangle with vertices…

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