Then
That is,
And so
So the Jacobian is
And so the required iterative system is
which is
with
Can you help me? This is calculus 3. Use Lagrange multipliers to find both the maximum and minimum values of f(z, y, z) = 2x + y-2z on the sphere r2 + y2 + z2-4. Use Lagrange multipliers to find both the maximum and minimum values of f(z, y, z) = 2x + y-2z on the sphere r2 + y2 + z2-4.
(1 point) Consider the vector field F(x, y, z) = (2z + 3y)i + (2z + 3x)j + (2y + 2x)k. a) Find a function f such that F = Vf and f(0,0,0) = 0. f(x, y, z) = b) Suppose C is any curve from (0,0,0) to (1,1,1). Use part a) to compute the line integral / F. dr. (1 point) Verify that F = V and evaluate the line integral of F over the given path: F =...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+y2- 1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x -0.9y-z 2 x2+ y2- 0.9. Solve the following problem...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2- 1 (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x-0.9y-z =2 x2+y2- 0.9 Solve the following problem using Lagrange...
Prove that the following vector field F = 4xi +z j +(y – 2z)k is a gradient field, which means F is a conservative field and the work of F is path independent? Show all your work. a) Find f(x,y,z) whose gradient is equal to F. Is the line integral ſi. · di path independent? b) Find the line integral, or work of the force F along any trajectory from point Q:(-10, 2,5) to point P: (7,-3, 12).
Construct and evaluate a surface integral that represents the work done by the vector field F(x, y, z)-(x, 2z, 3y), around the triangular section of the plane 2x + y + z traversed counterclockwise. 8 in the first octant Construct and evaluate a surface integral that represents the work done by the vector field F(x, y, z)-(x, 2z, 3y), around the triangular section of the plane 2x + y + z traversed counterclockwise. 8 in the first octant
p x + y+ 2z Subject to x+ 2y + 2z 60 2x +y + 3z 60 +3y+ 6z s 60 Maximize x, y,z 2 0 p x + y+ 2z Subject to x+ 2y + 2z 60 2x +y + 3z 60 +3y+ 6z s 60 Maximize x, y,z 2 0
Use matrices and row operations to solve the following system of equations: 2x-y+3z=7 x-y-z=0 -3x-2z=-11
Use matrices and row operations to solve the following system of equations: 2x-y+3z=7 x-y-z=0 -3x-2z=-11
x + y + z = 6 2x - y - z=-3 3y - 2z = 0 Question 1 (3 points) 1. X = 3. z = Blank 1: Blank 2: Blank 3: Question 2 (2 points) Picture or screenshot of your answer to #1 (from the matrix calculator). BIU E SÅ S T 2