.2 .2 ind the maximum and the minimum values of f(x,y,z) = 6x- 8y + 8z.on the sphere x +y +z = 164. The maximum value is (Simplify your answer.)

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

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

Q: Let (S) be the part of the sphere (x – 3)² + y² + (z – 1)² = 4 tha Then (S) is the graph of the…

A:

Q: 5. Prove that whole length of the curve x3 + y2/3 = a/3 is 6a.

A: Given that x23+y23=a23 To find the length of the curve:…

Q: (b) By minimizing the function f(x, y, u, v) = (1 – u)² + (y – v)² subject to the constraints y =…

A:

Q: 3/2 Find the length of the curve. y = (x* +4)" OSxs2

A: see below the answer and calculation

Q: 2 The length of the curve y = 312 between x = 0 and x = 1 is 3 %3D %3D

A: Answer is 4√2/3 unit.

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: Which of the following is the total length of the curve of intersection of the surfaces x2 + y? + 22…

A:

Q: Find the maximum and minimum values of the function ƒ(x, y) = 3x + 4y on the circle x2 + y2 = 1.

A:

Q: d) Consider the following equation of non-negative integers, x1, 12, T3 Ssuch that r1+12+ T3 = 20.…

A:

Q: Sketch the section of the surface at x = 0. y? - 25z? = 25 12 -12 -8 12 -4 -8 -12 4 -6 -2 -4 4.

A: topic - hyperbola

Q: Find absolute maximum and minimum values for f (x, y) = x² + 14xy + y, defined on the disc D = {(x,…

A:

Q: Find the points on the surface x² + y² + z² = 4 farthest from the point (1,–1,1), 2 %D

A:

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 8x – 6y on the circle…

A:

Q: 3. Describe the level surfaces of the function. f(x, y, 2) = x² + 4y? + 42?

A: We Know that,  A level surface of a function w = f(x, y, z) with three variables is a surface f(x,…

Q: The set of points P(x, y) such that their distance from (3, 0) is v2 times their 1. distance from…

A: The   distance from point Px,y  to 3,0 is 2 times the distance from point Px,y  to 0,2. Solution:…

Q: 2. Evaluate dy, where C is the part of the parabola y = x² from (1, 1) to (2, 4).

A:

Q: 2 2 15. Eind. the Poiats.an.the.. surface.Xy 2=1 that.are closest.bothaorrqin.

A: Lagrange method is another optimisation method. When a non-linear function needs to be optimised, we…

Q: Suppose that f(z, y) = z² - zy + y? – 5z + 5y with z? + y? < 25. 25 1. Absolute minimum of f(x, y)…

A: We have to solve the maxima minima problem.

Q: Given the expression x⁴-3x+7=y³ on the interval [3,5], determine the surface of revolution if it is…

A: Given that, the expression is x4-3x+7=y3.

Q: 8., (x + y) dA, where R is the region that lies to the left of the y-axis between the circles x? +…

A: As you have asked to answer question 8, we will answer question 8.Question 8.The given integral…

Q: Show that the minimum distance from the origin to a point on theplane ax + by + cz = d is

A: Given: ax+by+cz=d we know that minimum distance p of a point x1,y1,z1 from given equation of plane…

Q: What is the shortest distance from the point (4,0, 5) to the sphere (x – 1)2 + (y + 2)2 + z² = 36?…

A:

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: If a bug walks on the sphere x^2 + y^2 + z^2 − 4x + 4y + 4z + 3 = 0 how close and how far can it get…

A:

Q: Find the extreme values of g(x,y,z) = 2x² + xy + 4y² + xz + z² + 2. %3D and determine whether the…

A:

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

A:

Q: (d) | (3+ecos (0 sd AX ·

A: As per your query the solution of the problem (a) has been done in midpoint rule. For the solution…

Q: Determine the maximum and minimum values of f(x,y,z) = 3x + 6y + 2z, subject to 2x^2 + 4y^2 + z^2 =…

A: Using the lagrange multipliers

Q: 2 Find the points on the cone z = x´ + y´ that are closest to the point (2,-3,0)

A:

Q: What kind of surfaces are the level surfaces f(x, y, z) = const? f = 4x - 3y + 2z

A: As per the question we are given a trivatiate function : f(x, y, z) = 4x - 3y + 2z And we have to…

Q: 2. Sketch the level surface of the function w = f(x, y, z) = 25 – x² – (z – 2)² for w = 9.

A: 2. Sketch the level surface of the function w=fx,y,z=25-x2-z-22 for w=9.

Q: to the surface x 2 ^ 2A k. = i+

A:

Q: Suppose f(x, y) = x² + y² – 6x and Dis the closed triangular region with vertices (6, 0), (0, 6),…

A: Given,                             f(x, y)=x2+y2-6x                                  (1)and D is…

Q: 4. Evaluate where C is a circle of radius 2, parallel to the r - z plane and around the y-axis with…

A: Using the parametric equation of the curve C.

Q: Find the points on the cone 2 = r² + y? that are closest to the point (4, 2, 0). (Hint: You can…

A: Here we use the distance formula  D=(x2-x1)2+(y2-y1)2+(z2-z1)2 where D is the distance between the…

Q: What is the minimum value of the function f (x, y) = e*y on the set D = {(x, y) | 16x? + y² < 1}?…

A: Given function is fx,y=e-xy  on the set D=x,y: 16x2+y2=1

Q: c) Find the maximum value(s) of the function f (r,y, z) = x-2y+5z on the units sphere.

A:

Q: 9- Suppose T degrees is the temperature at any point on the sphere x² + y² + z² = 4 and T = 50x²yz.…

A: The temperature is

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

A:

Q: Find the maximum and minimum values f(1, y) = zy takes on the circle %3D r + y² = 12.

A: Lagrange multipliers method: First solve the following systems of equations: ∇fx,y=λ∇gx,y. The…

Q: 20. Find the minimum value of ry+xz+ yz given that r, y, z are real numbers that satisfies the…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Find the absolute maximum value and absolute minimum value of f(x, y) = x² + 2xy – 4x + 2y? – 8y +…

A: We have to find the absolute maximum and absolute minimum value of the given function.

Q: 13. Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y,…

A:

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. Given the expression x* – 3x + 7 = y* on the interval [3,5], determine the surface of revolution…

A:

Q: Find the absolute maximum and minimum values of fon the set D. (x, y)-xy2 + 4 D- ((x, y) Ix2 0, y z…

A:

Q: 4. Find the extreme values of the function f(x, y, z) = xy + z^2 on the circle of intersection of…

A: We first find the extreme values of the function fx,y,z=xy + z2 on the circle of intersection of the…

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.