Solve using Lagrange multipliers. 22. Find the points on the surface xy – z? = 1 that are closest to the origin.

Q: Find the point on the plane 3x + 2y + z = 6 closest to the origin. (Hint: Use Lagrange multipliers.)

A: Given plane is, 3x+2y+z=6, we need to find the point on this plane closest to the origin.

Q: Find the maximum value of f(x,y,z)=2x+5y+13z on the sphere x²+y²+z²=36

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Q: Consider the region enclosed by the curves y = r² + 1 and y = 2r + 1:

A: Consider the region bounded by the curves y=x2+1 and y=2x+1 The intersection between the curve is,…

Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

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Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

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Q: Find the area of the ellipse cut from the plane z = cx (c a constant) by the cylinder x2 + y2 = 1.

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Q: Suppose the temperature at the point (x, y, z) on the sphere x2 + y2 + ?2 = 16 is T= 800xy2z3 .…

A: Solution is given below:

Q: Use Lagrance Multipliers, and find the point P(r, Y, z) closest to the origin on the plane 2x + y –…

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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: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Use Lagrange multipliers to find the points on the given surface that are closest to the origin.…

Q: Find the area of the portion of the paraboloid z=x^2+y^2 that lies inside the cylinder x^2+y^2=4.

A: Given that ,  paraboloid   z=x2+y2 cylinder        x2+y2=4

Q: Find the average height of the paraboloid z = x+y over the square 0sxs1, 0 sys1. The average height…

A: Here in this problem we are given                                      z=x2+y2  ,0≤x≤1 and 0≤y≤1We…

Q: c) x+2y) dA, where D is bounded by the parabolas y=2x2 and y =1+x?.

A: C) The area D bounded by the parabolas y=2x2 & y=1+x2 is as shown below. The red graph is of…

Q: Q3. A- Use Greens theorem to evaluate the cireulation or flus for the velocity fiekd : S(x, y)=- *+y…

A: Given velocity field is  f(x,y)=1x+yi-1x+yj we have to find the flux for the boundary of square…

Q: Q2 (a) Find the volume under the surface z = 3x3 + 3x²y and over the rectangle R = {(x,y):1 < x <…

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Q: Which bowl holds more water if it is filled to a depth of four units? • The paraboloid z =x? + y?…

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Q: 11. What is the equation of the surface revolved about the x-axis for 2² - xz = ln x + 3x? A. y²…

A: Introduction: When a surface is revolved around the coordinate axis, another surface is obtained. In…

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 +y? + 2? = 1 is T =…

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Q: If the maximum distance from the surface x? + 2y² + z? = 3 to the point (1,0, –1) is Va+ bv6, what…

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

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Q: Find the point on the plane 3x + 2y + z = 6 closest to the origin. Hint: Use Lagrange multipliers.

A: The given plane: 3x+2y+z=6 To find the point on the plane 3x+2y+z=6 closest to the origin. Solution:…

Q: 10. If ZYXW is an isosceles trapezoid with WY = 15x-2 and XZ = 9x + 10, find x. X 1 partn Z Y

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Q: Find the area of the surface. The part of the paraboloid z = x² + y2 that lies inside the cylinder…

A: Area of the surface f(x ,y) above a region R of the xy-plane is given by…

Q: (8) Find the point(s) where the line r(t) = ti+(1+t)j+5k intersects the paraboloid z = x² + y?.

A: A detailed solution is given below.

Q: et T(x, y, z)= 100+ x² + y² represent the temperature at each point on the sphere x² + y² + z² = 80.…

A: Given: Tx,y,z=100+x2+y2sphere g= x2+y2+z2=80plane h =x-z=0

Q: (a) Compute the area of the portion of the cone x2 + y2 = z? with z 2 0 that is inside the sphere x2…

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Q: Find the points on the cone z^2=x^2+y^2 closest to the point (4, 2, 0).

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Q: Find the point on the line y = x closest to the circle of radius 1 and center (5, 2) using Lagrange…

A: Please refer to the image below

Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

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Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Given data:   The given expression is y2=36+xz.   The expression of the distance of a point from the…

Q: Graph the surface 1 = y? +z? - by first sketching at least three cross sections in each of the xy…

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Q: Find the extreme values of z on the surface 2x² + 3y2 + z2 - 12xy + 4xz = 35.(DO NOT USE LAGRANGE…

A: For the solution follow the next steps.

Q: Find the points on the cone z 22 = x2 + y? that are closest to the point (-3,1,0)

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Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: Find the area of the surface. The part of the paraboloid x = y² + z² that lies inside the cylinder…

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Q: The temperature in space given by T (x, y, z) = 200xyz². Find the hottest temperature on a unit…

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Q: Find the maximum value of  f(x,y,z)=27x+7y+3z on the sphere x2+y2+z2=81

A: For this question we will use Lagrange multipliers where f(x,y,z)=given function and…

Q: Find the surface area generated by rotating the semi-circle x = (49 – y² be- tween -7 < y < 7 about…

A: To Determine :-  The surface area generated by rotating the semi-circle x = 49 - y2 between -7 ≤y ≤7…

Q: 47. Find the distance between the spheres x? + y² + z² = 4 and x? + y? + z? = 4x + 4y + 4z – 11.

A: The equation of the spheres are given:

Q: Evaluate ||| Vx² + y² + ²²&V where S lies above the cone z = Vx² +y° and between the spheres x + y…

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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: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: to Rind the points Lagrange multiplier surface (x-1)(y-2)(Z-)=| near est Qz use on the to the point…

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Q: Find the maximum value of f(x,y,z)=9x+14y+29z on the sphere x2+y2+z²=25

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Q: Find the minimum distance from the surface to the given point. (Hint: Start by minimizing the square…

A: The minimizing function is, d2=(x-8)2+y2+z2

Q: 11r If F(r) and o is the surface (x – 4)2 + y² + z² = 49 oriented 3 outwards, what is the value of…

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Q: (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the area of the part of the paraboloid x = y2 + z2 that lies inside the cylinder y2 + z2 = 1

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Q: 3. Find the area of the surface cut from the paraboloid x? + y +z = 2 by the plane y = 0.

A: Here we have to find the area of the surface cut from the paraboloid x2+y+z2=2 by the plane y=0.

Q: Below is a curve C, which is the intersection between the surfaces  S1 : z = 4 − x2 S2 : z + 2x −…

A: Given that,Below is a curve C, which is the intersection between the surfaces   S1 : z=4−x2  S2 :…