(x² +2y) where D is the triangular region with vertices (0, 1), (1,2) and (4,1).

Q: Use Lagrange multipliers to find the distance from the point (3, 0, -1) to the plane 6x - 4y + 7z +…

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Q: f (x, y) = x² + y² – 2x, D is the closed triangular region with vertices (2, 0), (0, 2), and (0, –2)

A: According to the given information, it is required to find the absolute maximum and minimum values…

Q: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x +…

A: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x + y…

Q: 24 dA - I 3x – Y when D is the parallelogram bounded by x – 2y = 0, x – 2y = 2, - and Зх — у 3D 1,…

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Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: 3. Find the shortest distance between parallel planes 2x - 3y + z = 4 and 4x -6y + 2z = 5.

A: Given equation of planes: 2x-3y+z=4 and 4x-6y+2z=5. To find: Shortest distance between the parallel…

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

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Q: Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that…

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Q: Use the Method of Lagrange Multipliers to find the largest product that the positive numbers x, y,…

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Q: Use the method of Lagrange multipliers to find three positive real numbers, x, y, and z whose…

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Q: F = (-3y, 3x); R is the triangle with vertices (0, 0), (1, 0), and (0, 2).

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: Find the minimum value of x²+y² + z²,

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Q: 8. The distance between the planes 2r -y-2z 5 and 2r - y- 2z = 7 is A C 2 D 4

A: As the planes are parallel than for calculation distance between planes we use formula:…

Q: (d) [[x - y dA where R is the triangular region with vertices (3, 10), (3, 0) and (-2, 0).

A: Use double integral

Q: Z=N34-9x-4y p.) Draw the Surface in 3 dimensions

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Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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Q: Find the line of intersection between the two planes x+2y-z = 5 and x-4y+z=3

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Q: Find two nonnegative numbers x and y with 2x + y = 3 for which the term xy² is maximized. by

A: Given 2x+y=30, we need to maximize xy2

Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what…

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Q: Use the method of Lagrange multipliers to find the shortest distance from the point (-2, –3, 1) to…

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Q: The graphs of r +y² + 6x – 24y + 72 = 0 and x² - y' + 6x + 16y - 46 0 intersect at four points.…

A: We have to find distance from given point to intersecting points of given equation. And then add all…

Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0.

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Q: Use the Lagrange multiplier method to find the point on the plane 4x +3y +2z = 0 with the smallest…

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Q: Use Lagrange multipliers to find the shortest distance, d, from the point  (1, 0, −2)  to the plane…

A: Lagrange Method:- The method of Lagrange multipliers is a strategy for finding the local maxima and…

Q: C is counterclockwise around the rectangle with vertices (0, 0), (5, 0), (5, 3), (0, 3) (a) directly…

A: The given integral is: ∮xy dx+x2 dy C is the counterclockwise around the rectangle with vertices…

Q: 4y² dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

A:

Q: A point moves in the (x, y) plane on the line 2x+ 3y −4 = 0. Where will it be when the sum of the…

A: We have to find a point from where the sum of square of its distances from 1,0 and -1,0 is smallest.

Q: 9-The distance d between the parallel planes -2x+y+z 0, 6x-3y-3z-5-0 is: a) V54 b) 54 V5 d) 3 c) e).…

A: Distance between two parallel lines

Q: Use Lagrange multipliers to find the point on the plane  x − 2y + 3z = 6  that is closest to the…

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Q: 3. Use LaGrange multipliers to find the point on the plane 2r - y+4z = 10 that is closest to the…

A: Use Lagrange method to find point

Q: 4) Find line of intersection for 2 planes.  2x-3y+z=5 -x+2y+3z=2

A: We will solve the problem

Q: Find the maximum value of f(r, y) = 10ry(4 – 8z - 4y) over the triangle with vertices (0, 0), (,0)…

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Q: 19. y² dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

A: 19. Given D is the triangular region with vertices (0, 1), (1, 2), (4, 1).We find the given double…

Q: Use the Lagrange multiplier method to find the point of the plane 4x-5y+3z=1 with less distance to…

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Q: Find the total length of the loop of the curve 6y^2 = x (x - 2)^2 between x = 0 and x = 2.

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Q: 5. Use the method of Lagrange multipliers to minimize f (x, y) = x2 + y? subject to 2x + 8y 102.…

A: The given question is related with Lagrange multipliers . We have to minimize fx , y = x2 + y2…

Q: Use Lagrange multipliers to find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme…

A: This question is related to Lagrange multipliers theorem. We will solve this question by using…

Q: Enclosed by the cylinders z= x2 y = x 2 and the planes  z =0 y =4

A: Given: The cylinders z= x2 y = x 2 and the planes  z =0 y =4 The solid enclosed by the surfaces,

Q: 1. Trapezoid JKLM with vertices J(-6, 6). K(-3,7), L(-1.3), and M-8, 0): (x, y) (x+7, y-3) J'() K'…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Use the method of Lagrange multipliers to maximize 2x + 3y – 4 on the circle x² + y? = 13

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Q: Minimize Z=8x+12y subject to 4x+6y214, 4x+5y9, x>0, y20 M=?

A: Given LPP is Minimize  Z = 8x + 12y Subject to  4x + 6y ≥ 14, 4x + 5y ≥ 9, x ≥ 0, y ≥ 0

Q: Find the maximizer of f(x, y) = x² + y² subject to 2x + y ≤2, z ≥ 0 and y ≥ 0.

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Q: If & is the solid tetrahedron with vertices (0, 0, 0), (3, 0, 0), (0, 5, 0) and (0, 0, 4) then: z dV…

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Q: dx Calculate for n = 6, using trapezoidal rule. %3D -11+ x²

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Q: What are the perpendicular generators on (D) 등 =D3 %3D (P) -= of the surface

A: Given equations are  x216-y24=z ......(1)x3=y2=z-4  ......(2) Equation of generators of the…

Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…

Q: 3. Use the method of Lagrange multipliers to find the highest and lowest points on the surface x^2 +…

A: To find the highest/lowest points actually we have to maximize/minimise the value of z , within the…

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (Hint: To simplify the…

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Q: To describe the triangular region whose vertices are (0,0), (2,2), and (-2,2) we use the following…

A: We have to describe the triangular region whose vertices are 0,0,2,2 and -2,2