MATH 121 Midterm: MATH 121 Amherst F14M121 280203 29Benedetto

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 121
• Professor: All

Document Summary

Final exam december 19, 2014: this is a closed-book examination. No books, notes, calculators, cell phones, communication devices of any sort, or other aids are permitted: you need not simplify algebraically complicated answers. 2 , eln 4, e ln 5, ln(e7), 3: [15 points] evaluate each of the following limits. 5 x(cid:19)(cid:21)x: [20 points] evaluate each of the following integrals. (a) z x arcsin x dx (b) z 4 3. For each of the following improper integrals, determine whether it converges (a) z . 8x + 41 dx (b) z 2. 1 x ln x dx (c) z . 1 x2 + 3x + 2 dx (d) z 1. Find the sum of each of the following series (which do converge): ( 1)n 6n+1. 2n+1 (ln 3)n n! (c) ( 1)n 2n (16)n (2n + 1)! In each case determine whether the given series is absolutely convergent, (a) (d)