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

Q: Identify and sketch the surfaces x2 + y2 - z2 = 4

A: Given, The surface is x2 + y2 - z2 = 4

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: To find the minimum distance from the given curve to the point using Lagrange multipliers method.…

Q: Q:3 Find the minimum distance from the surface x + y°-z = 1 to the origin.

A: The minimum distance from the surface

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y3…

A: We know that area of surface generated by revolving the curve y=f(x) about x-axis from x=a to x=b is

Q: Find the minimum distance from the point to the plane x - y + z = 3.

A: Now, formula of shortest distance of the plane ax+by+cz=d passing through the point (l, m, n) is,

Q: Find the points on the surfaces z = V² + y? and z = 2 – x/2 having the shortest distance to the…

A: We know that the two given surfaces will intersect at some curve whose equation can be obtained by…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. =x²+²x≤x≤1 3x 2…

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Q: Find the points on the surface y = 4 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

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Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: Find the Exact Area of the surface obtained Retating by the curve asout the X-axis 9x=18+g2 25Y56

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Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

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Q: Find the minimum distance from the parabola a – y? = 0 to the point (0, 3). Minimum distance =

A: Find the distance using distance formula and then differentiate to get the minimum value equate the…

Q: Find the points on the surfaces x^2-yz=25 that are closest to origin

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Q: Find the minimum distance from the point to the plane x- y +z = 6. (1, -6, 2)

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Q: Find the minimum distance from the parabola x – y = 0 to the point (0, 3). Minimum distance = %3!

A: At P(x,y), the point of shortest distance the slope of the line from P to (0,3) must be…

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: Which point on the curve y = Vx – 1 + 8 is closest to the point (5, 8)? (x, V) = ( What is this…

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Q: Find the minimum distance from the parabola y=x^2 to point (0, 3)

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Q: Find the exact area of the surface obtained by rotatingthe curve about the x-axis. 9x =y2 + 18 ,  2…

A: Consider the curves, 9x=y2+18,  2≤x≤6 Differentiate the given curve with respect to “y” then,…

Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

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Q: What is the shortest distance from the surface xy +12x +z^2 =144 to the origin?

A: To find the shortest distance from surface xy +12x +z2 =144  to origin.

Q: Find the minimum distance from the point (-6, -6, 0) to the surface z = O√√559 O 3√61 09 O√773 O√69…

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Q: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

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Q: Find the points that are minimum to the origin and lie on the lines of intersection of planes: y +…

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

A: Given surface equation is

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: (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 minimum vertical distance between parabolas y = x2 + 4 and y = x -x2

A: Given: The equations of two parabolas are: y1=x2+4 y2=x-x2 We have to find the minimum vertical…

Q: Find the minimum distance from the point to the surface z = V7 - 2x – 2y. (Hint: To simplify the…

A: We need to find the minimum distance from the point A (-2,-2,0) to the surface z = 7-2x-2y…

Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

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Q: Find the area of one side of the “winding wall” standing orthogo-nally on the curve y = x2, 0 <=x…

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Q: Q6) (Lagrange Multipliers) to the origin Find minimum distance from the surface r? – y – 2? =1

A: The solution is given below in the next step:

Q: Q1 Find extrema point of the Surface 2-ペ-S-12x+3}+2

A: Consider the given function  z=x3-y3-12x+3y+12 Find partial derivatives of the function with respect…

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0 ≤ x ≤ 1…

A: The formula for the surface area of the rotating object from the curve y=f(x) with the constraint…

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0< x <1…

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Q: Find the minimum distance from the surface x2 -y2 -z2= 1 to the origin.

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

A: The plyboard has dimensions 3×5 ft2 So, the area of the board is 15 ft2 The area of the shape needed…

Q: The area of the surface obtained by rotating the curve y = 36-x2, -6<xS6 about the x-axis is

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

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Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,

Q: Find the minimum distance from the point (0, 0, 4) to the surface  z = (1-2x-2y)^1/2   (Round your…

A: Solution:

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

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Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x< for -2 <x<…

A: To Find

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.