MATH 121 Final: MATH 121 Amherst F15M121Final

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

Document Summary

December 20, 2015: 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, ln(e7), e ln 5, 3: [15 points] evaluate each of the following limits. Be clear if the limit equals a value, + or , or does not exist. (a) ln(1 x) + arctan x lim (b) (c) x (cid:18)1 arcsin(cid:18) 6 x(cid:19)(cid:19)x lim x ln 3 lim x 0 xex. 9: [30 points] evaluate each of the following integrals. dx (using a trigonometric substitution) (b) z 3. 2 dx (d) z x arcsin x dx: [24 points] or diverges. For each of the following improper integrals, determine whether it converges. 8x + 12 dx = z 1. 8x + 19 dx: [18 points] Find the sum of each of the following series (which do converge): (a) Xn=0 ( 1)n+1 2n+1 (ln 6)n n! (d) .