MATH 250 Final: MATH 250 Amherst S17M250Final
15 Feb 2019
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Final exam may 11, 2012: 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, or e3 ln 3 should be simpli ed. sin(cid:16) . 6(cid:17), 4: please show all of your work and justify all of your answers. (you may use the backs of pages for additional work space. , [15 points] evaluate each of the following limits. Be clear if the limit equals a value, + or , or does not exist. (a) lim x 0. 3xex arctan(3x) x + ln(1 x) (b: [30 points] evaluate each of the following integrals. x (cid:18)cosh(cid:18) 1 lim x(cid:19) . 5 x(cid:19)x (a) z ex (e2x + 4) 2 dx hint: e2x = (ex)2 (b) z x arcsin x dx (c) z x4 + 5x2 x + 3 x3 + 3x dx: [20 points] or diverges.
