MATH 201 Exam 1, Fall 2012

Math 201 Quiz 1 (Time: 65 minutes) (Fall 2012) N. Nahlus Name: ……………………………………….. (VERY CLEARLY) I.D ........................................... Circle your Section number (- 3 points if incorrect) Sec 8 (12:30 T) — Sec 9 (2:00 T) — Sec 10 (11:00 T) — Sec 11 (5:00 T) --- Sec 12 (9:00 M) — Sec 13 (3:30 R) — Sec 14 (10:00 M) — Sec 15 (5:00 R) --- Investigate = Investigate (with justification) convergence or divergence of the following series. In LCT problems: IF you know the answer of L=simply write the answer without proof. 1. (24%) (a) Investigate (b) Investiagte given that (c) Investiagte given that Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Total over 100 d) Investigate (Hint: Write as exponential. Then use exp. Series.) 2a) (9%) Find Hint : Use (if this last exists) . Moreover, 2b) (10%) Find the open interval of convergence Do not check end-points 3) (19%) a) (10%) Find the Maclaurin series of to deduce 3b) (9%) Find the exact value of (Hint: Differentiate the series 4) (19%) Suppose converges, prove or disprove that converges 4b) Suppose converges, prove or disprove that converges 4c) If for all n, investigate convergence/divergence of (Hint: First, find ) 5) (19%) a) (8%) Find 5b) (6%) Suppose . Show that= its Maclaurin series for 0 < x < 1000 (Hint: Use Taylor’s Remainder’s formula ) 5c) (5%) Use the Maclaurin series of