Question

Find the linearization L(x,y,z) at P_0. Then find the upper bound for the magnitude of the error E in the approximation f(x,y,z) = L(x,y,z) over the region R.

The linearization of f(x,y,z) at Po is L(xyz)=_______

Answer 1

L(xyz) = ( 1 , 3 , -7 )

L = x + 3y - 7z -3

Explanation:

f (x,y,z) = xy + 2yz - 3xz

f (3,1,0) = (3) (1) + 2 (1) (0) - 3 (3) (0)

f (3,1,0) = 3

fx = y - 3z

f (3,1,0) = (1) - 3 (0)

fx = 1

fy = x + 2z

f (3,1,0) = (3) - 2 (0)

fy = 3

fz = 2y - 3x

f (3,1,0) = 2 (1) - 3 (3)

fz = -7