• The set of points in the plane where a function f(x, y) has a constant value f(x, y) = c is called a level curve of f. What is the level curve f(x, y) = 2 of the function f(x, y) = x? + y? – 4? %3D а. line b. circle c. parabola d. point а. d.

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A: Given that the shape for a building that is to become a wheat silo created by rotating the region…

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Q: Given z = f(x, y) = V² + y² + 4y. (a) Find its domain and range. (b) Sketch the level curves for z =…

A: Introduction: Assume D is a subset of R2. A rule that assigns each pair (x,y) in D a value z=f(x,y)…

Q: Given z = f(x, y) = Vx2 + y² + 4y. (a) Find its domain and range. (b) Sketch the level curves for z…

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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,…

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Q: Find minimum distance from the surface x² – y? – z² = 1 (Lagrange Multipliers) to the origin.

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Q: A5: What is the minimum (perpendicular) distance from the point p = (-1,–2) to the line L := 4x = 14…

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Q: Sketch a typical level surface for the function f(x,y,z) = y? +z?. .. Choose the correct graph of a…

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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: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for −1 ≤ x…

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Q: · What is the shortest distance from the surface xy + 6x + z = 41 to the origin? distance =

A: The surface is given as , xy+6x+z2=41 find the shortest distance from the surface to the origin.

Q: Find a formula for a functionf(x, y, z) whose level surface f= 3 is a cylinder of radius 5 centered…

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Q: et f(z, y) = for (z, y) # (0,0). Find the level curves of 2 + y²

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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: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

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

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Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: The line y = mx +b intersects the parabola y = x^2 at points A and B. Find the coordinates of the…

A: The line y=mx+b intersects the parabola y=x2 at the pointsA and B.Let A=x1,x12 and B=x2,x22, where…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

A: We have to calculate the area of the smaller region bounded by x+52=2y from left sides,and bounded…

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: Find the positively oriented simple closed curve C for which the value of the line integral     (y3…

A: The line integral is  ∫C(y3 − y) dx − 9x3dy The expression for Green's theorem is  ∫CP(x,y) dx…

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Q: Find the area bounded by the curve y= 16 (A) 8 square units (B) 4 square units (C) 10 square units…

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Q: The region in the first quadrant bounded above by the line y = 6, below by the curve y = √6x, and on…

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Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

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Q: Find the minimum distance from the curve y = 2 to the point P(6,0)

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Q: Find the points on the surface y2 = 4 + xz that are closest to the origin. (Enter your answers from…

A: Consider the given surface equation y2=4+xz.  The distance d between the origin 0,0,0 and any point…

Q: 2. Noemi had a 3 × 5 ft² piece of plyboard. She needs to have it cut it into a parabolic shape that…

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Q: Given z = f(x, y) = Va2 + y² + 4y. %3D (a) Find its domain and range. (b) Sketch the level curves…

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Q: (a) Find the area of the surface generated by the given curve about x-axis y = V, (b) Find the area…

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Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

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Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

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Q: Find the area bounded by the curve y = 16 (A) 16 square units B 8 square units C 4 square units D 10…

A: Given  y = x316-34x2 + 3x  ------(1) y =x                             -------------- (2)

Q: (a) Sketch the contour plot of f(x, y)= Y using the level curves of height k = -2, -1, 0, 1, 2. X…

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Q: Q/ Find the points have minimum distance from the origin to the surface. xyz²=1

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Q: Find a curve in the xy-plane passing through the origin andwhose slope at the point (x, y) is x + y.

A: we have to find a curve in the xy-plane passing through the origin and whose slope at the point (x,…

Q: 2. Noemi had a 3 × 5 ft² piece of plyboard. She needs to have it cut it into a parabolic shape that…

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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: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

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Q: Describe the level curves of f(x, y) = x + 2y Sketch the level curves for c = ±1, ±2, ±3, ±4.

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Q: What is the maximum vertical distance between the line y = x + 38 and the parabola y = interval [–…

A: Given line equation is y=x+38 Given parabola equation is y=x2 From the above two equations x2-x-38=0…

Q: 3 Find the area bounded by the curve y=-x3- 16 A) 8 square units (B) 10 square units C 4 square…

A: The region is bounded by the curves y=116x3-34x2+3x and the line y=x

Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

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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: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

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