MATH 121 Final: MATH 121 Amherst F13M121 280103Benedetto 29Final
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Fall, 2013 devices of any sort, or other aids are permitted: this is a closed-book examination. No books, notes, calculators, cell phones, communication: you need not simplify algebraically complicated answers. , arctan(cid:0) 3(cid:1), 43/2, eln 4, ln e7, e ln 5, e3 ln 3, or cosh (ln 3) should be simpli ed: please read each question carefully. Show all of your work and justify all of your answers. (you may use the backs of pages for additional work space. ) as sin. Be clear if the limit equals a value, + , , or does not exist. (a) lim x 0 (b) lim x sinh x x arctan (4x) e4x + 1. Evaluate each of the following integrals. (a) z 2 3. 2 dx (c) z x4 + 2x2 + x + 2 x3 + 2x dx. For each of the following improper integrals, determine whether it converges or diverges. 1 x2 8x + 41 dx (b) z 9.