For each surface T(u, v), identify the best description of the surface's shape. F(u, v) Shape <и, и, и + v > a. parabolic cylinder < cos(u), v, sin(u) > < v², u, v > < v cos(u), v, v sin(u) > b. plane c. cylinder d. cone

Q: z =x' +y° +1 Y L x' +y? -z? = 1 LY

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Q: 2. State the names of the following quadric surfaces. (a) The surface z = y² – 2x². (b) The surface…

A: a. this equation is in form of  as sign of A and B is opposite it is  Hyperbolic paraboloid

Q: Determine the projection of the following surface on the xy plane *- y+ =1 O parabola ellipse O…

A: To determine the projection of the given surface on the xy-plnae.

Q: The surface described by the conditions 2 + y? + z² = 4, x 0 is the same as the surface described…

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Q: 8.2

A: We know that,

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: What is the equation of the surface revolved about the x-axis for z? – xz = In x + 3x? A. y? + z? =…

A: Given that z2-xz=lnx+3x The objective is to write the equation of the surface revolved about x axis.…

Q: Find the following: The traces of the surface x2 + y? + 22 = 6 in the planes parallel to the…

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Q: Find the traces of the given surface in the planes x=k,y=k,z=k. Identify the surface and sketch it.

A: The given surface is 4x=y2+z2 We have to identify the surfaces in the planes x = k,  y = k and z =…

Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: Given: x2+y42+z2=1  ……1   Equation of plane is: z=14  ……2

Q: Consider the surface z = (x+ 1)² + (y – 2)² – 1 - Select a correct name for this surface and point…

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Q: Find the area of the surface cut from the paraboloid x² + y² -z = 0 by the plane z = 6. The surface…

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Q: Identify the surface defined by the following equation. 2x-y +z? = 0 The surface defined by the…

A: Form of equation               Surfacex=Az2+By2                     Eliptic Praboloidx=Ay2-Bz2…

Q: Find the traces of the given surface in the planes x=k,y=k, z=k. Identify the surface and sketch

A: Quadric Surface Hyperboloid of two sheet z2c2-x2a2-y2b2=1 In this two variables have negative…

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: For the surface 4x² +2²-y²=9, classify the trace when z = 1. O line O hyperbola O ellipse O parabola

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Q: cribe the surface with equation x + y° + z? + 8x + 4y + 2z – 43 = 0 surface is a sphere with center…

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Q: Describe and provide a rough sketch of the surface determined by the following equation: -x² +4y? -…

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Q: w.The given.surface.at. thespeeif 2.

A: Introduction:   We know that the equation of tangent plane to the surface z=f(x,y) at the point…

Q: Consider the surface defined by the equation 2.x2 – 2y2 – z = 0. (a) Choose any one of the variables…

A: The equation is the form z=f(x,y) represents a surface in the space. In this problem the equation of…

Q: 18. Find the surface area of the part of the sphere x² + y² + z² = 4 that lies inside the cylinder…

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Q: Determine the projection of the following surface on the xz plane. (xz trace) 4z – + = 0 O Parabola…

A: Solution is given below:

Q: Determine the projection of the surface – y? = z on the yz-plane? (Hint: a = 0) Circle O No answer…

A: The solution is :

Q: Find the area of the following surface using a parametric description of the surface.   The cap of…

A: Consider the surface that is the cap of sphere:

Q: Determine the projection of the surface - y = 3. on the yz-plane? (Hint: x = 0) O Parabola O No…

A: Given:      Surface x23-y2=z       By putting x=0 we get             023-y2=z

Q: 9a2 + 4y? + 36z? = 36 %3D

A: given surface 9x2+4y2+36z2=36 claim- to find the trace of given surface in planes x=k , y=k , z=k ,…

Q: Let (P) be the surface given by the following equation z = 5-x²-y² and (Q) be the surface given by…

A: Given surface P is, z=5-x2-y2    ----(1) For xy projection, put z=0 in (1) we get, 0=5-x2-y2⇒…

Q: Find the traces of the given surface in the planes x=k,  y=k, z=k. Identify the surface and sketch…

A: The given surface is 4x=y2+z2. We have to identify the surfaces in the planes x = k,  y = k and z =…

Q: Sketch the surface given by the equation x2+z2/3+y=3 indicating the points where the surface…

A: Sketch the surface given by the equation x2+z2/3+y=3   indicating the points where the   surface…

Q: Match the equation with the surface it defines. f(x, y) = -√√x²+12 X O O O stisk 3

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: 2? = a? + 2y?

A: Consider the given surface z2=x2+2y2 The trace in the plane x=k are z2-2y2=k2 For k=0, z2-2y2=0⇒…

Q: For the surface 4x² + y² −z = 0, classify the indicated trace as an ellipse, hyperbola, or parabola.…

A: We have been given the equation  4x² + y² −z = 0           (1)

Q: 9. Reduce the following equation to one of the standard forms, classify the surface, then sketch the…

A: General equation of an ellipsoid is given by, (x-p)²/a² +(y-q)²/b² +(z-r)²/c²= 1

Q: Plot the surfaces over the indicated domains. Ifyou can, rotate the surface into different viewing…

A: The given equation is   z=x2+2y2at-1≤x≤1and-2≤y≤3

Q: Let f(x,y)=/4– 4x² – y² . Find its domain and give a rough sketch of its surface.

A: The given function is:fx, y=4-4x2-y2To find domain and sketch the surface

Q: Match the equation with the surface it defines. Also, identify each surface by type. 1. x = y? - z2;…

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Q: Which of the following is a non-orientable surface? O a. all the other choices are orientable O b.…

A: orientable surface -  The surface for which we can define clockwise consistently.

Q: 16. classify the surface: * 1- y? = 5x2 + 6z? Sphere Elliptic paraboloid Cone Plane Ellipsoid

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Q: What are the reace curves of this surface for x=0, y=0, and for z=k? Name the shape of the surface.…

A: Note : In the question it has to be '' trace curves '' instead of '' reace curves ''. So, we are…

Q: Given a surface, f(x,y,z)=15, explain what you would do to find the equation of the tangent plane at…

A: Procedure to find tangent plane at a point on the surface:

Q: Match the graph of the surface with one of the contour maps. f(x, y) = el=x*+y

A: Graph of given multivariable function is

Q: Sketch the portion of the surface that lies in the first octant: y = z. 0.15 0.a 0.1 0. 0.15 0.18

A: To sketch the portion of the surface y=z that lies in the first octant. The sketch of y=z is:

Q: p(x, y, z) = e¬x²-y²–z² +2yz

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Q: Find the traces of the given surface in the planes x = k, y = k, z = k. Identify the surface and…

A: Given - The surface z = x2 - y2 To find - The traces of the given surface in the planes x = k, y =…

Q: The tangent plane to the graph of the surface z=In(x2+y?) at the point (1,0,0) contains point…

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Q: Given the surface r(u,v) =  (0 ≤ u ≤ 5, 0 ≤ v ≤ 4pi) Explain clearly what gridlines are found when…

A: Given surface is ru,v=ucosv,usinv,v To find the equation of tangent plane for u=3, v=8π3…

Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…

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Q: Identify the surface by completing the squares. x + 4y? – 2 – 6x + 8y + 4z = 0 O An elliptic…

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Q: Sketch the following, and identify the surface by name. Show all your work, including all traces. x2…

A: solution given below

Q: Name the surface and draw an accurate Graph of z = xʻ in R’.

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