59. Let f(x, y) = x². %3D (A) Explain why the cross sections of the surface z = f(x, y) produced by cutting it with planes parallel to y = 0 are parabolas. (B) Describe the cross sections of the surface in the planes X 0, x 1, and x = 2. (C) Describe the surface z = f(x, y).

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

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Q: Sketch the following surfaces. 1) 4x^2+9z^2=9y^2 2)y^2-x^2=z Show all work.

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Q: Sketch or describe the surfaces in R³ of the equation presented x² + y} – 2x = 0

A: The equation is x2+y2-2x=0

Q: sider the surface z = f(z, y)=√√/25 - 1² - y².

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Q: Consider the surface O3z+3y-2z=0 O 34z + 7y-12z = 0 O 3x+3y-2z=147 What is the equation of the…

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Q: 2. Consider the surface defined by 1² + 2xy + y² + 2²-25 Let F(x, y, z)-1² + 2xy + y² + 2². (a)…

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Q: (10) Let f(x, y) = /x-y a) Find the domain and range of f (x, y). Sketch the domain on the x-y…

A: Step:-1 Given that fx, y =x-y Part (a):- The square root function is real when x-y≥0 x-y≥0⇒x≥y⇒y≤x…

Q: A surface has Cartesian equation :- f(xy). given by f(1.9)=6xy-5x -3y+ +7x-6y a) Use any…

A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

Q: 6. Sketch the surface x² - + 4 4 (a) What are the traces of this surface in the plane x = C (where C…

A: The equation of the given surface is  .(a) To find the traces of this surface in the plane .(b) To…

Q: For f(x, y, z) = x^2 − 6x + y^2 + z^2 , describe and draw the level surface for the function value…

A: Let w=f(x,y,z) . The level surfaces of w=f(x,y,z) results, when w=k slices the the function,…

Q: Find the center and radius of the sphere given by the equation x^2 + y^2 + z^2 + 4x − 6z + 4 = 0.…

A: Given equation of a sphere x2+y2+z2+4x−6z+4=0

Q: 9) Sketch the graph of the equation y² +2²=1 and correctly identify the surface.

A: Given: The equation is y2-x24+z2=1. To sketch: The graph of the given equation. To identify the…

Q: Identify and use traces to sketch the surface 1. y= 9 - x2 - z2 2. y = 4 - z2

A: We will find traces on all 3 co ordinate planes , x=0 ,y=0 and z=0 . then draw the surface  Note :…

Q: The slope of the surface z = ry² in the r-direction at the point (2,3) is slope of this surface in…

A: The slopes of the surface: z=f(x, y) in the x, y directions at x0, y0 are fxx0, y0, fyx0, y0.

Q: f(x,y)=9-x^2- y^2

A: We have to find standard form of the given equation and then identify the surface

Q: 16. Consider the equation of the surface S given by z = 3r*ya + 3y – 4 Where a is an even number and…

A: Linear approximate equation is the equation of tangent plane.

Q: Find the equation oftangent plane and normal lines ofthe surface: f(x,y, z) = 10x² –14 y² +11z³-7 at…

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Q: Which of the following is the coordinates of all points on the surface with equation z = x³-5xy¹…

A: To find the coordinates of all points on the surface where the surface has a horizontal plane, we…

Q: Describe and sketch the surface given by the function.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Describe and sketch the following surfaces z = f(x, y): (a) * (c) 2= /1-x² - y² z = 6 - 2x - 3y (b)…

A: We have to sketch and describe the following curve

Q: show several surface levels of f(x,y)= (x+y)/(x-y) and graph a contour map with solution

A: The given function is f(x,y)=x+yx-y. To Sketch: various level surfaces and contours.

Q: Consider f(r, y) = /1– 2² – y². (a) What is the domain of f ? That is, for which (r, y) does the…

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Q: (a)) The base point of the surface is (0,0,0) and its axis (of symmetry) is the line (x, y, z) = (0,…

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Q: 2) Describe the level curves of the surface Z = √36 4X² 9Y²

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Q: Describe the surface whose equation is given by x² + y² + z² + 6y - 2z = 0.

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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: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3

Q: The surface of a paraboloid results from rotating a parabola about its axis. the parametric form is…

A: The objective of the question is to understand how the shape of a paraboloid changes when the…

Q: 2 2 f(x, y) = 4x² - y² a) Sketch traces for some values of f(x, y) = k, xz-trace and yz-trace, and…

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Q: 1. Find the equation of the tangent plane for the implicitly defined surface xy + xz+yz = 1

A: First we arrange the equation of the surface into the form  f(x,y,z)=0 xy+xz+yz-1=0

Q: Name the surface and draw an accurate Graph of y = x² + z² in R'.

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