Classify and Sketch the surface X2+ Zy² + Z? -4x+4y-2z+3:0

Q: Describe and sketch the surface x + 2y + 3z = 6

A: Given

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: 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 highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…

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Q: Find the area of the surface. The part of the surface z = 9 + 5x + 2y2 that lies above the triangle…

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Q: find a parametrization of the surface. The paraboloid z = x2 + y2, z<=4 The paraboloid z = 9 - x2…

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Q: Describe and sketch the surface (x2/16) + (y2/9) + z2 = 1

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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: The parametric representation of the surface x² – 8x + z? = 0,0 < y < 5 is a) ř(u, v) = (4 cos u , 4…

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Q: sketch the given surface. x2 − y2 + 9z 2 = 9

A: Given, x2-y2+9z2=9

Q: Sketch the surface: x + 2y + 3z = 12.

A: First find the intersection of plane with axis then draw the plane.

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: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

Q: Classify and sketch the surface x − y2 − 4z2 = 0.

A: The surface is given as x-y2-4z2=0. Rewrite the equation x-y2-4z2=0 as follows. x-y2-4z2=0x=y2+4z2…

Q: Classify the surface: 1- x = 3y? + 4z2 O Plane O sphere O cone O Elliptic paraboloid O Ellipsoid

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Q: Sketch the surface z = 3x? + y? +1 and find its linear approximation at P-(0, -1)

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

A: The given quadratic surface is  x2+y42+z2=1 , y=0

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: Sketch the quadric surface: r +4y2 +4z2 16. Note: The x, y, & z axes are depicted in red, green, &…

A: The given function is: x2+4y2+4z2=16

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

A: Given that: z=x2+y2      ......(1)z=25-x2-y2      ......(2)

Q: The parametric representation of the surface y2 - 4y + z2 = 0,0 < x < 3 is a) 7(u, v) = (v, 2 + 2…

A: solution:y2-4y+z2=0 , 0≤x≤3considery2-4y+z2=0∴y2-4y+4+z2=4∴y-22+z2=22

Q: Sketch the surface z = f(x,y). f(x.y) = 4x² + 4y² + 2 OC. OD.

A: Given function is fx,y=4x2+4y2+2. We have to sketch the surface of fx,y=4x2+4y2+2.

Q: Evaluate F dS, S where 4 F(x, y, z) = (3y, -2x, -), and S is the surface that is composed of 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: Identify and sketch the surfaces z = - (x2 + y2)

A: Identify and sketch the surfaces z = - (x2 + y2)

Q: The parametric representation of the surface x² – 6x + z² = 0,0 < y < 2 %3D is a) (u, v) = (3 cos u…

A: The general form of the parametric equation of the surface in three-dimensional space is given by…

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: Verify Stoke's theorem for A=(2x-y)i-yz²j-y*zk where S is the upper half 5A. surface of the sphere *…

A: Consider the given vector and sphere equation. A→=2x−yi−yz2j−y2zk and x2+y2+z2=1 Since S is the…

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

A: To solve this we will use divergence theorem.

Q: Sketch the surfaces 1. . z = x2 + 4y2  2. x = 4 - 4y2 - z2 3. x2 + y2 = z2

A: The given surfaces are sketched using online 3D calculator.

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: Locate and classify the stationary points on the surface z=xy2-2xy-2x2-3x, remembering that  x, y ,…

A: Solving for stationary points of given function using partial derivatives

Q: Describe the surface. x² + z² = 1 O sphere O ellipsoid O hyperboloid O circular cylinder O elliptic…

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Q: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 − z2 − 2x…

A: x2 + y2 − z2 − 2x − 4y − 4z + 1 = 0

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: Let C be the intersection of the surface x² + y² + z² cylinder x² + 3y² = 4, z > 0. = 9 and the

A: As per the question we are given the equation of a sphere and a cylinder (with elliptical cross…

Q: Describe and sketch the surface in R3 represented by  a. 2x+z=3 b. z=cos y

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

A: To sketch the given surfaces.

Q: Evaluate | F-dS, where F(x, y, z) = (3y, –2x, –), %3D and S is the surface that is composed of the…

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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: Plot the implicitly given surface (x − 1)² /4 + (y − 1)² +z² = 1 (a) using the sphere function. (b)…

A: As per the question we have to plot the following surface : (x-1)2/4 + (y-1)2 + z2 = 1 With the help…

Q: Sketch the surfaces 1. z = y2 - 1 2. 4x2 + y2 = 36

A: Using graphing calculator to sketch themz=y^2-1

Q: The parametric representation of the surface y2 - 4y + z2 = 0,0 <x< 3 %3D is a) F(u, v) = (v, 2 + 2…

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Q: The parametric representation of the surface x2 -8x + z2 = 0,0 < y 5 5 %3D is a) (u, v) = (4 cos u ,…

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Q: Identify the surface y-3=x²+z² paraboloid cylinder cone hyperboloid

A: y-3=x²+z²

Q: Find a parametrization for the intersection of the surfaces: z = x2 + y2 and  x2 + 4y2 = 1

A: Find the parametric representation for the intersection of the given surfaces.

Q: Sketch the surfaces 1.z = 1 + y2 - x2  2. z =-(x2 + y2 ) 3. 4y2 + z2 - 4x2 = 4

A: Used graphing calculator to graph:z = 1 + y^2 - x^2 from two viewing angles

Q: 7. Sketch the surface 1≤z≤2-x² - y²

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.