a.Find the maximum value of w = xyz on the line of intersection of the two planes x + y + z = 40 and x + y - z = 0. b. Give a geometric argument to support your claim that you have found a maximum, and not a minimum, value of w.

Q: Q2/ Examine the following surface for maximum , minimum, and sa z = x3 – 3x? – 4y2 + 2

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

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Q: Find the maximum and the minimum values of f(x.y.z) = 9x- 9y +2z on the sphere x +y +z = 166.

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Q: +3そ20 22 Prove that the line X21+2t ニー+3t is perpendicular to the plane X-2y+zz6

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: 18. Let f(x, y, z) = 2x + 4y – 4z. Find the minimum and maximum values on the sphere x2 + y² + z² =…

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Q: Q2/Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y…

A: We can use the second derivative test to find the maximum, minimum and saddle points.

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A: (a) Given information:

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Q: (a) y= -2 (d) xy = 0

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

A: solutionGivenT(x,y,z)=100+x2+y2x2+y2+z2=30plane x=2

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Q: Find the maximum and minimum values of f(x, y) = x² + 2y² on the quarter circle x² + y² ≤ 4 with r,…

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Q: Q2/ Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y…

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Q: Find the lengths of the curves in Exercises 13–14. 13. y = x^1/2 - (1/3)x^3/2, 1<=x<= 4 14. x…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

A: Given: Tx,y,z=100+x2+y2 represent the temperature at each point on the spherex2+y2+z2=40. To Find:…

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Q: 1. Find the absolute minimum value of 0 < x < 4 f (x, y) = 4x² + 2xy – 2y? – 18x on the rectangular…

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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: 2.2 Find the maximum and the minimum values of f(x,y,z) = 5x – 3y +7z on the sphere x +y +z = 83. 2

A: Here we find the maximum and minimum value of f(x, y, z)

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Q: 3.4.8 Show that the sphere x² + y² + z² = 1, z ≥ 0. JJ,z²dS=, where S is the surface of

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A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: ii) Prove that the straight line y = x is the curve giving the shortest distance between the points…

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Q: Test the following surface for maxima., minima. And saddle points: Z = x2 + x y+ y2 + 3 x- 3 y+4

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Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure…

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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: a) Find maximum and minimum of F(x, y, z) = 2x+y-2z with constraint G(x, y, z) = x² + y² /2+z² = 1.…

A: Given F(x,y,z)=2x+y-2z and G(x,y,z)= x2+y2/2+z2=1

Q: Let (m, n)be the point at which a line is tangent to the ellipse + m = 1lf this line has x-intercept…

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Q: Find the maximum value of f(x,y,z)=9x+15y+9z on the sphere x2+y2+z²=100

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Q: Find maximum,minimum,and saddle point of the surface Z= x³-y³-12x + 3y + 12.

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Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure…

A: Since you have submitted two questions, we\'ll answer the first question. For the second question…

Q: Find the absolute maximum and minimum values of f(r, y) = r-3r-y+12y, closed region D, where D is…

A: Given problem:-  Find the absolute maximum and minimum values of f(x, y) = x²-3x-y³+12y, on the…

Q: Find the maximum value of f(x,y,z)=24x+18y+21z on the sphere x²+y²+z²=49 I

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Q: Q1/ Find maximum,minimum OULE ,and saddle point of the surface Z = x³y³ - 12x + 3y + 12.

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Q: Consider the parabola f (x) = x² – 4x and the line g(x) = –2x – 1. Determine the %3D point(s) of…

A: Given parabola,y=x2-4x                     (1)Given line y=-2x-1                     (2)Put value of…

Q: Q2/ Examine the following surface for maximum , minimum, and saddle points z = x3 – 3x2 – 4y² + 2

A: Take the first order and second-order partial derivatives of z with respect to x and y.

Q: (a) Use the method of Lagrange multipliers to determine the minimum and maxi values of f(x, y) = x²…

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Q: 1. Using the lagrange multiplier method, find the maximum and minimum temptaure of he plate whose…

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Q: Sketch the graph of the following quadratic surfaces a) 4x² +9y² + z² = 36 b) x² - y²z² = 1 c) x²…

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

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.