MTH 234 Study Guide - Midterm Guide: Cylindrical Coordinate System, Tangent Space, Directional Derivative

• School: MSU
• Department: Mathematics
• Course: MTH 234
• Professor: B.Mackey

Document Summary

3x (e) none of the above: let f = x2 + 3xy where x = v + sin u and y = u + sin v. which of the following is true? (a) (b) (c) (d) = (3u 2v + 2 sin u + 3 sin v)(cos u) + ( 3v + 3 sin u) 2x y: if dr dt, evaluate the limit if it exists. 4 x2 (cid:90) 3: if f (x, y, z) dz dy dx = (cid:90) 3 (cid:90) a (cid:90) b f (x, y, z) dx dy dz then a = and b = 4: (4+10+6=20 points) let f = (cid:104)2x + y + yz, x + xz, xy + 1(cid:105). (a) show that curl(f) = 0. (b) find a potential function f such that f = f. (cid:90) 5: (8+8=16 points) evaluate the integrals (cid:90) 1 (cid:90) 1 (a)