MATH 450 Final: MATH 450 Amherst S18M450Final
15 Feb 2019
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Final exam may 14, 2016: 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: [18 points] evaluate the following limit. Be clear if the limit equals a value, + or , or does not exist. (a) lim (b) lim x 0 xex arctan x ln(1 + 3x) 3x x (cid:18)arcsin(cid:18) 1 (c) compute lim x 0. 1 x(cid:19)x x(cid:19) + e xex arctan x ln(1 + 3x) 3x again using series: [18 points] evaluate each of the following integrals. (a) z. 1 (x2 + 4)2 dx (b) z 0. 1 x4 arcsin x dx: [36 points] or diverges. For each of the following improper integrals, determine whether it converges. 1 x4 x3 + 3x2 x + 2 x3 x2 + 3x 3. 1 (d) z 4 x2 8x + 19.
