MATH 200 Study Guide - Midterm Guide: Spherical Coordinate System, Iterated Integral, Directional Derivative

• School: UBC
• Department: Mathematics
• Course: MATH 200
• Professor: All

Document Summary

[9] 1. (a) consider the plane 4x + 2y 4z = 3. Find all parallel planes that are distance 2 from the above plane. 27 px2 + y2 + z2 + 3. What is the rate of change of t (x, y, z) in this direction? (i) use linear approximation of t at the point p to approximate t (1. 9, 1, 1. 2). (iii) let s(x, y, z) = x + z. Find and classify the critical points of f (x, y) = 3x2y + y3 3x2 3y2 + 4. Use lagrange multipliers to nd the minimum and maximum values of (x + z)ey subject to x2 + y2 + z2 = 6. Consider the domain d above the x-axis and below parabola y = 1 x2 in the xy-plane. (a) sketch d. (b) express. Z zd f (x, y) da as an iterated integral corresponding to the order dx dy.