# 02spex3 - MATH 222 THIRD MIDTERM 9:55am10:45am Your Name...

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MATH 222 — THIRD MIDTERM April 10, 2002, 9:55am–10:45am Your Name: Your TA: (circle one) Chris Alfeld Graham Jonaitis Andy Raich Joshua Rushton Fernando Miranda Score 1: 2: 3 or 6: 4: 5: Total: THIS EXAM HAS SIX PROBLEMS YOU SHOULD ONLY DO FIVE OF THESE EVERYONE MUST DO PROBLEMS 1,2,4,5 YOU MUST CHOOSE BETWEEN PROBLEMS 3 AND 6 DO EITHER 3 OR 6 BUT NOT BOTH 1
2 (1) Find the solution of the differential equation dy dx = (1 + y 2 ) sin x, which satisfies y ( π 2 ) = 3.
3 (2) Find the solution of the differential equation x dy dx + (1 - x ) y = 1 - x which satisfies y (1) = 0.
4 Do either this problem or problem 6 (on polar coordi- nates) but not both (3) In the problems on this page x is an abitrary real number. (a) Compute z = x + i 7 + i (i.e. write z as a + bi with a and b real.) (b) Assuming x > 0, draw x + ix 3 and compute arg( x + ix 3) (c) Assume 0 < x < π/ 2. Draw e ix , e 2 ix and e ix + e 2 ix in one figure. Then compute z = e ix + e 2 ix , i.e. rewrite z = a + bi with a and b real. [Continue on reverse side]