Currently need help with part b and part cPart A was already answered (https://www.bartleby.com/questions-and-answers/a-compute-the-equation-of-the-tangent-plane-to-the-level-surface-9x-y-2-xy-2yz-3zx-3-dont-rou-1were-/d852afc6-18f6-42ac-aa27-8a7b369c0a5c) a) Compute the equation of the tangent plane to the level surfaceg(x, y, z) = x'y + 2y°z – 3z*x = 3Don't round answers unlessat the point (1,0, – 1).b) Consider z = z(x, y) as a function of x and y, so z(1,0) = -1. Usethe approximation of the surface by its tangent plane to approximate21 = z(0.99, 0.02).c) Use your approximation of z1 from part b to evaluate g(0.99, 0.02, zı)to five decimal places. Your answer should be close to 3. Is it?the instructions request approximations, or as part of checking yourown work.

Name: Currently need help with part b and part cPart A was already answered
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: Currently need help with part b and part cPart A was already answered (https://www.bartleby.com/questions-and-answers/a-compute-the-equation-of-the-tangent-plane-to-the-level-surface-9x-y-2-xy-2yz-3zx-3-dont-rou-1were-/d852afc6-18f6-42ac-aa27-8a7b369

The equation of the tangent plane is 3x-9y+z-2=0. Then, the function is z=-3x+9y+2 The approximation of the surface by its tangent is given by L ( x , y ) = z( 1 , 0 ) + zx ( 1, 0 ) ( x−1 ) + zy ( 1, 0 ) ( y − 0 ) Then, zx=-3 and zy=9 L ( x , y ) =-1 -3( x−1 ) + 9y Substitute the point: z1=0.99, 0.02 L ( 0.99 , 0.02) =-1 -3( 0.99−1 ) + 90.02=-0.79With the approximation, the point is 0.99, 0.02, -0.79. Substitute it in gx, y, z=x3y+2y3z-3z3x: g0.99, 0.02, -0.79=0.9930.02+20.023-0.79-3-0.7930.99≈1.48372 No, it is not close to 3.