Question: 12. Use the method of Lagrange multipliers to solve Problems 36. 3. Find the minimum distance from the surface x2 + y2 :2 = l

12. Use the method of Lagrange multipliers to solve Problems 36. 3. Find the minimum distance from the surface x2 + y2 :2 = l to the origin. 4. Find three numbers whose sum is 9 and whose sum of squares is as small as possible. 5. Find the hottest point (x. y. 2) along the elliptical orbit 4x2 + y2 + 4:2 :16 where the temperature function is T(:c,y,z) = 8x2 + 4y: 16: + 600 6. A Least Squares PlaneGiven the four points (xk . yk. 5k) (0.0,0).(0.1.1),(1,1. l).(1.0,1) nd the values of A. B, and C to minimize the sum of squared errors 4 Ewe + BM + c at)? k=l if the points must lie in the plane 2=Ax+By+C \\O")

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