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

Q: Find the maximum value of f(x,y,z)=15x+y+6z on the sphere x²+y²+z²=441

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Q: B- Find all local extreme values of the following surface. f(x, y) = 2xy – x² – 2y? + 3x + 4.

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

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Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x A. y² + z² =…

A: Given: The equation z2-xz=lnx+3x which is of surface and is quadratic for z.  To find: The equation…

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.

Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

A: Given: The equation of surface which is z2-xz=lnx+3x. This equation is a quadratic equation for z.…

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

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Q: sketch the given surface. x 2+ 9y 2 + 4z 2 = 36

A: To sketch the given graph

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

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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: 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: Q3/ Examine the following surface for maximum and minimum points z = 2x2 + 3xy + 4y² – 5x + 2y

A: Since you have posted multiple question according to company rule we are supposed to give solution…

Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

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Q: Find the minimum of f(x,y) = 5x + 4y on the ellipsoid 6x2 + 4y2 = 3. Leave your answer correct to t…

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Q: Identify and sketch the surfaces x2 + (y - 1)2 + z2 = 1

A: given: the equation of the surface x2+y-12+z2=1

Q: Find the minimum of f(x,y) = 3x + 4y on the ellipsoid 6x2 + 2y² = 3. Leave your answer correct to…

A: Solution of the problem as follows

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

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Q: A surface in R³ is defined by the equation 4z = x² + 4y².

A: Given:-                 The surface in  is given by  . Sketch the intersections (traces) of this…

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

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Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

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

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

A: Given :- z=x3 -y3 -12x+3y+12 Find:- Maximum, minimum and saddle point of the given surface

Q: Q3: Find the points on the surface x^2+z^2-2=0, closest to the origin.

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Q: Find the maximum and minimum values of a function F(x,y.z)3D8X+y+ z on the surface A

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Q: Q1: Find the maximum and minimum point on the surface f(x,y)= 5xy-7x -y² +3x -6y +2

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Q: Find the minimum of f(x,y) = 5x + 2y on the ellipsoid 9x2 + 2y2 = 7. Leave your answer correct to…

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Q: Q3/ Sketch the surface z 3x2 + y? +1 and find its linear approximation at P.(0,-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: 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: Evaluate ∬S(x2+y2)dS, where S is the surface z=4−x, 0≤x≤2, 0≤y≤2.

A: Given z=4-x , 0≤x≤2 ,0≤y≤2 to evaluate ∬Sx2+y2dS where S is surface

Q: What kind of surfaces are the level surfaces f(x, y, z) = %3D const? 9. f = 4x – 3y + 2z 10. f =…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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 maximum value of f(x,y,z)=25x+3y+17z on the sphere x2+y2+z²=100

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

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Q: Find the point on the surface r² – 2ry + 2y² – x +y = 0 closest to the point (1, 2, –3).

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Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

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: 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: Maximize 2x + 3y+ 5z on the sphere x +y +z=19.

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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: Q2 Find the maXimum and minimum values of aFunction FCXS.2) = 8x+j+ 2 en the Surface x+y, z"=18 %3D

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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: Q3: Find the local maximum, local minimum, and saddle points of the surface f (x, y) = %3D 2x3 –…

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Q: Find the points on the surface z²2=xy+1 that are closest to the origin using LaGrange multipliers

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Q: 4) Let h(x, y) = 2x² + y² – 2x²y. Find the absolute minimum and maximum values of the surface on the…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.