Sketch the level surface of the function w +z = 9 – r² when w = 0 for z > 0.

Q: Let f (z, y) = 4x+y. Find the slope of the surface z = point (1, -1). f (T, y) in the y-direction at…

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

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Q: Find a function f (x, y) that has the line y = 3x - 4 as a level curve.

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: Identify the surface and find the traces of the following function: x^2 = y^2 + z^2

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Q: Sketch the region in the xy-plane defined by the equation or inequalities. (a) -1sys3 (b) |지 < 4 and…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

Q: Sketch in the two level curves of: f (x, y) = y+ x² = k _for k = 1, 2.

A: Solution is written in below steps.

Q: f(x, y, z) = x² + 3y² + 5z?

A: Let us assume f(x,y,z)=x2+3y2+5z2=k Assume that k≠0 x2+3y2+5z2=k Divide both sides by k,…

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: Let C be the curve y = 8/a for 2.1 < x < 3.8.

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Q: Classify all level curves of f(x, y) = Vy² – x² and draw its contour map.

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Q: What is the largest vertical distance between the graphs of the functions y = Va and y x2 in the…

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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: 3. Describe the level surfaces of the function. f(x, y, 2) = x² + 4y? + 42?

A: We Know that,  A level surface of a function w = f(x, y, z) with three variables is a surface f(x,…

Q: Describe the level curves of: (a) f(x, y) = e4x-y (b) f(x, y) = In(4x – y) (c) f(x, y) = 3x² – 4y2…

A: (a) To decribe the  level curvesf(x, y)=e4x-y = 1 , 2 , 3, 4, 5

Q: Sketch a contour diagram for f(x, y) = x2 − 2y2 with three labeledcontours.

A: To sketch the contour diagrams for the given function of two variables

Q: The area, in square units, bounded by the curves y = x² , y=2 – x and y=1 is ,

A: For a bounded figure, to find the area we need to determine the limits and the curves we need to…

Q: Describe the level surfaces for f (x, y, z) = y+10-√√x² + z² and sketch them for several (at least…

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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 maximum value of f(x, y) = 4x + 6y subject to being on the circle = 13. 5. x² + y

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Q: Identify and sketch the surfaces x2 + (y - 1)2 + z2 = 1

A: given: the equation of the surface x2+y-12+z2=1

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

A: Given fx,y=x2-y

Q: What is the maximum vertical distance between the line  y = x + 30  and the parabola  y = x2 for…

A: Definition used -                  Vertical distance is given by -…

Q: Find the length of the curve y = x2 from x = 0 to x = 7.

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Q: Show that the maximum value of f (x, y) = x 2 y3 on the unit circle is

A: We should maximize f(x,y)=x2y3 under the constraint gx,y=x2+y2 where x2+y2=1. Now, ∇f=2xy3,…

Q: Describe and draw at least 3 level surfaces for the function f(r, y, z) = x²+ y? - z?

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Q: Use the contour map to estimate 8g/8z at the point (V8,0) for the function g(z, y) = 9-2-y2.

A: ∂g∂x =limh→0 fx+h,y-fx,yx+h-xAt x,y ≡ 8,0   (The  point on Red contour line)fx,y  = 1       (The…

Q: What is the largest vertical distance between the graphs of the functions y = v and y = x in the…

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Q: Describe the level surfaces of the function.  f(x,y,z) = x+4y+5z

A: Consider the function: fx,y,z=x+4y+5z

Q: Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by…

A: Given data÷ F(x,y)= 8x2+8y2 Now , we have to draw z=8x2+8y2

Q: Sketch the contour plot of f(x, y) = 4x² + y² using level curves of height k = 0, 1, 2, 3, 4, 5.

A: Given: f(x,y)=4x2+y2 Let 4x2+y2=k. Now graph contour plot for k=0,1,2,3,4,5.

Q: Find the image of the line y =-x under the mapping = f(z) =2² + 4z %3D %3D

A: We need to find the image of the line y = - x under the given mapping.

Q: Justify why the level curves very close to the origin (0,0) for the function f(z, y) = (1-z)(1 – )…

A: As per the instruction, we will be solving the first question. For (1), We are given the function as…

Q: Q3 Determine the area of a surface when the curve y==x² 3 1 x², 1<x<3, is revolved about 2 the…

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Q: What kind of surfaces are the level surfaces f(x, y, z) = const? f = 4x - 3y + 2z

A: As per the question we are given a trivatiate function : f(x, y, z) = 4x - 3y + 2z And we have to…

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: 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: Find the area of the surface generated when the curve f(x) = (2/3)x^(3/2) - (1/2)x^(1/2) ; [1,9] is…

A: Given:

Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: Given w = f (x, y, z) = 4.x² + y² + 4z². Sketch the level surface of the function for w = 1.

A: We have to sketch the level surface of the following function for w=1, w=f(x,y,z)=4x2+y2+4z2

Q: Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by…

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

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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: Calculate the area of the surface generated when the curve, f(x) = x3/2 – on [1,2 ] is x'/2 revolved…

A: The surface area will be given by S=∫ab2πy1+dydx2dx

Q: Find the absolute maximum value and absolute minimum value of f(x, y) = x² + 2xy – 4x + 2y? – 8y +…

A: We have to find the absolute maximum and absolute minimum value of the given function.

Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2

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: Find the local minimum value of f(r, y) = 4+ a7 + y7 – 7xy.

A: We need to find the local minimum of the equation.