MATH1003 Midterm: MATH 1003 UNB Exam 1003 05
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Read this first: 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. , 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. ) Be clear if the limit equals a value, + , , or does not exist. (a) lim x 0 sinh x x arctan (4x) e4x. [10] (b) x (cid:18)1 sin(cid:18) 5 lim x(cid:19)(cid:19)x. [16] (a) z cos x (1 + sin2 x) For each of the following improper integrals, determine whether it converges or diverges. 1 x[9 + (ln x)2] dx (b) z e. Find the sum of each of the following series (which do converge):
