3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the xy-plane with vertices (0,0), (2,1), and (0,1).

Q: Find the area of the surface x2 + y2 - z = 0 that is cut from above by the plane z = 4

A: Surface is given by x2+y2=z Area=∫∫R2x2+2y2+1dA       =∫∫R4x2+4y2+1dA Let x=rcosθ and y=rsinθ…

Q: Find the surface area of the portion of the paraboloid given by the equation z = 1– x2 – y² that is…

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Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

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Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

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Q: 6 Consider points P and Q in the x-y plane, with P = (1,0) and Q (0,1). The line integral %3D %3D Q…

A: Introduction :Given, two points P and Q .P= (1,0)Q= (0,1)We have asked for the line integral of

Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x A. y² + z² =…

A: Given: The equation z2-xz=lnx+3x which is of surface and is quadratic for z.  To find: The equation…

Q: 5. Use traces to sketch and identify the surface x2- y? - z2 = 4.

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Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

Q: Sketch the section of the surface at y= 0. z = V4 +x + y² 41 -8 -6 -4 -2 -4 6.

A: Let's find.

Q: B Suppose we want to find all the points on the surface gx, y) x+ 4y - 4 where the tangent plane is…

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

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Q: Consider the normal line to the surface z = x2 + y² (paraboloid) at the point P(1, 1, 2). Find the…

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Q: 17. Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1x 4, 0 y < 1

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Q: 14) Find the points on the surface xy- z2 = 1 that are closed to the origin. %3D

A: To find the point on the below surface that is closed to the origin. xy−z2=1

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: Find the shortest distance between the surface z = x² + y² and the plane r + y – z = 4.

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Q: 1. Find the area of the surface the part of the plane 3x + 2y + z = 6 that lies on the first octant

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Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

Q: 5. Find the surface area of the portion of the surface z = 2x + y? that is above the triangular…

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Q: Determine the points on the surface y2 + z2 − x = 8 that are closest to the origin. Solve problem…

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Q: Find the points on the surface z2 = xy + 4 closest to the origin.

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Q: 2 Find the surface area of the portion of the cone x² + y² = 2² above the region inside the…

A: we have to find the surface area of the portion of the cone x2+y2=z2 above the region inside the…

Q: 1. Find the closest point of the surface ry + xz + yz = 1 to the origin. %3D

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

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Q: Sketch the section of the surface at y = 0. 1 + x² + y² Z = 4 -8 -6 -4 -2 4 4 6. 4 -8 -6 -4 -2 2. 4…

A: Given data is: To sketch the surface at y=0 z=1+x2+y2

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

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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: (a) Show that the two surfaces S₁: z = xy and S₂ : z = ³x² - y² intersect perpendicularly at the…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

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

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Q: sketch the given surface. x2 + y2 − z 2= 1

A: Given: x2 + y2 − z 2= 1

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: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

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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: 14. Under the paraboloid z=x² +y2 and above the disk x +y² <9 for (x,y) in the first quadrant.

A: we have to find the volume

Q: Graph the surface 1 = y? +z? - by first sketching at least three cross sections in each of the xy…

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Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

A: Given:- The equation of the surface revolved for the x-axis is, z2-xz=ln(x)+3x

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

A: Consider the provided question, We have to find the point on the given surface closest to the point…

Q: Sketch the trace curves of x^2 − y^2 + z^2 − 4x + 2z = 4, and use these trace curves to sketch the…

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Q: Q– Fin the surface area of the portion of the paraboloid z= 6-2x - y that is above the x-y plane…

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Q: Find the points on surface z^2=xy+4 closest to origin.

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

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Q: Are there any points on the hyperboloid x² – y² – 2² = 1 where the tangent plane is parallel to the…

A: By see this solution

Q: Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1 < x < 3, 0 < y < 1.

A: Given surface is z=f(x,y)=1+2x+3y+4y2 where f(x,y)=1+2x+3y+4y2 Differentiate f(x,y) partially with…

Q: Find out the nature of the surfaces 2x +3y² +z² –8x+6y-4z-3=0 and compute their centers and lengths…

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Q: Find the points on the curve of intersection of the ellipsoid x² + 4y² + 4z² = 4 and the plane x –…

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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: Identify and sketch the section of the surface at z = 0. v2 = 1 25 4 16 Type of the surface: too 4 4…

A: Solve the given

Q: Graph the surface 1 = y2 + z2 –- by first sketching at least three cross sections in each of the xy…

A: We have to sketch the graph of the following surface in the 3D space: . First we have to sketch the…