MATH1003 Midterm: MATH 1003 UNB Exam 1003 04
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May 9, 2017: 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: [12 points] evaluate the following limit. Be clear if the limit equals a value, + or , or does not exist. Simplify. (a) (b) compute lim x (cid:18)1 arcsin(cid:18) 5 x(cid:19)(cid:19)x lim x 0. 5xex arctan(5x) sinh x + ln(1 x: [16 points] evaluate each of the following integrals. (a) z cos x (cid:0)1 + sin2 x(cid:1) dx. 1 x arcsin x dx: [40 points] or diverges. For each of the following improper integrals, determine whether it converges. 1 x [9 + (ln x)2] dx (b) z e. 2 x2 6x + 8 dx (d) z . 1 x2 6x + 13 dx: [20 points] Find the sum of each of the following series (which do converge).
