If all of the level curves of a function f(x, y) are parallel lines, then the function must be linear, i.e.: the graph of the surface z = f(x, y) must be a plane. T/F + explanation

Q: sketch a typical level surface for the function. ƒ(x, y, z) = x2 + y2 + z2

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Q: Sketch a typical level surface for the function. 10) f(x, y, z) = /x2 –z %3D

A: sketch a typical level surface for the following 10) fx,y,z=x2-z it is known that level surface is…

Q: Find and sketch the level curves f(x,y) = c on the same set of coordinate axes for the given values…

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Q: Let f(r) = x and g(x) = (I – 4)“ + 5. There is one line with positive slope that is tangent to both…

A: The given function fx=x2gx=x-42+5 Since the tangent line is the same for both the equations…

Q: f(x, y) = /36 – x² – y², then the level curve f(x, y) = 7 is empty. - ect one: True False

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Sketch a typical level surface for the function f(x,y,z) =2x² + y? +z?. Vhich of the following is a…

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Q: Find the sketch of the level curve flx, v)-c form and f(x.y) 100-x2-y and c- 0.

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Q: (a) y= -2 (d) xy = 0

A: Consider the given information.(a)The given condition is y=-2.The line y=-2  is a vertical line,…

Q: Let f(x,y) = x* + y². Find the slope of the line tangent to this surface at the point (1,1) and…

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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: 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: f(x, y) = 3xr +2y. f(x, y) in the x-direction at the Find the slope of the surface z point (4, 2).

A: Slope of z-surface of a function in the x direction is defined by fxx,y [ derivative of f(x,y) w.r.t…

Q: find an equation for the level surface of the functionthrough the given point. ƒ(x, y, z) = √(x - y)…

A: given,  ƒ(x, y, z) = √(x - y) - ln z, (3, -1, 1)

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

A: The slope of the surface z=fx, y in the x-direction at the point is denoted by the value of partial…

Q: Let f(x, y) = x 2 − y. Sketch the level curves for f = −2, 0, 1.

A: Given fx,y=x2-y

Q: Q2: (a) Sketch the domain of f(x, y) = Vx + Vỹ on the ay-plane (b) Sketch the level curve of g(x, y)…

A: (a) To sketch the domain of f(x,y)=x+y The above function is defined only if x and y are…

Q: sketch a typical level surface for the function. ƒ(x, y, z) = ln (x2 + y2 + z2)

A: The given function is  ƒ(x, y, z) = ln (x2 + y2 + z2). In order to sketch the typical level surface…

Q: Find an equation for the level surface of the function f(x,y,z) = x? +y? +z? through the given point…

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Q: Let z=f(x,y) = y² – x³ . Find the slope of the line tangent to this surface at the point (-1, -2)…

A: Given surface is z=f(x,y)=y2-x3.

Q: Describe the level curves of the function z = 6 − 2x − 3y. Sketch a contour map of the surface using…

A: Given z=fx,y=6-2x-3y We need to sketch the level curves of the function fx,y

Q: Find the slopes of the surface in the x- and y-directions at the given point.

A: z=25-x2-y2, 3, 0, 4 Partially differentiating with respect to x, we get ∂z∂x=1225-x2-y2·∂25-x2-y2∂x…

Q: Find, sketch, and identify the surface of points composed of (a, b, c) for which g(a, b, c) = ab +…

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Q: Find an equation of the tangent plane to the surface at the given point. x2 + y? - 32? . = 82, (-7,…

A: Given equation  x2+y2−3z2=82,     (-7,-6,1)

Q: Pictured are a contour map of f and a curve with equation g(x, y) = 8. Estimate the maximum and…

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Q: Describe the level curves of the function f(x, y) = xy. Sketch a contour map of the surface using…

A: To Determine:  Describe the level curves of the function f(x, y) = xy. Sketch a contour map of the…

Q: Let f (x,y) = AS The level curve of f(x,y) = 10 is: %3D x2 +5y2" %3D O A circle An ellipse O A…

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Q: Given f(x, y) = 9-x² – y² a) Sketch the graph of f(x, y). b) Identify the surface and state the…

A: a)sketch of graph

Q: 2. Sketch the level surface of the function w = f(x, y, z) = 25 – x² – (z – 2)² for w = 9.

A: 2. Sketch the level surface of the function w=fx,y,z=25-x2-z-22 for w=9.

Q: Describe and sketch the surface given by the function. f(x, y) = y2

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

Q: • The set of points in the plane where a function f(x, y) has a constant value f(x, y) = c is called…

A: Given: fx,y=x2+y2-4

Q: A. Find an equation of the level surface of f(r, y, 2) = 4.x2 + 22 that passes through the point…

A: Given:     f(x,y,z) = 4x2 + z2      Point: ( 1 , 2 , 3 )

Q: Draw the level curves of a. f(x,y) = x2 + 3y2 (c-0, 2, 4, 6) %3D b. f(x, y) =1 (c=0, 0.2, 0.4, 0.6)…

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Q: find and sketch the point of shortest (or longest) distance from the origin of curve…

A: We need to find and sketch the point of the shortest (or longest) distance from the origin of curve…

Q: Let (m, n)be the point at which a line is tangent to the ellipse + m = 1lf this line has x-intercept…

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Q: If f(x, y, z) = V3x + y2 – 2z, then find the slope of the surface f in the x- direction at the point…

A: We are given a surface: f(x,y,z) = 3x+y2-2zWe need to find the slope of surface f in the x-direction…

Q: sketch a typical level surface for the function. ƒ(x, y, z) = x + z

A: Given ƒ(x, y, z) = x + z

Q: Describe and sketch the graph of the level surface f (x, y, z) = c at the given value of c = 9. f(x,…

A: Given  f (x, y, z) = c at the given value of c = 9 fx,y,z=x2+y2+z2

Q: Let f (x, y) = 4x° + y°. Find the slope of the surface z = f (7, y) in the y-direction at the point…

A: The given problem is to find the slope of the given surface in y-direction at the point (1,-1).

Q: C. Find the extrema of f(x, y) = x2 +y subject to x2 – y? = 1. Use a graph of the contours and…

A: Given:f(x,y)=x2+y   subject to x2-y2=1

Q: (a) Find the slope of the surface, f(x,y)=1-(x-1)² -(y-2)² at the point (1, 2, 1) in the x-direction…

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Q: Q3: Find the local maximum, local minimum, and saddle points of the surface f (x, y) = %3D 2x3 –…

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Q: Describe the graph of the level surface y f (x, y, z) = x² + z at the given value of c = 1 4

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Q: Let f(x.y) = x° +y*. Find the slope of the line tangent to this surface at the point (- 1, - 1) and…

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Q: Let f(r, y, z) = r² – 21 + y² – z. (a) Show that the equation of the level surface that passes…

A: The given function is: f(x,y,z)=x2-2x+y2-z (a) The level surface is given by: x2-2x+y2-z=c...(1)…

Q: a) Find the point of intersection of the curves y = x and y = 2 – x.

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Q: Let f(x, y) = x2 + 2y. Sketch the level curves for f = −2, 0, 1.

A: Level curves: A level curve is defined as the cross section of the graph of z=fx,y taken at a…

Q: Let z=f(x,y) = y x². Find the slope of the line tangent to this surface at the point (-2, -1) and…

A: 5.

Q: A student is graphing the function y= Vz+4 on the coordinatė plane. Which statement will help the…

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