Bounded - Calculus Two - Solved Exam, Exams of Calculus

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“APPM 1360 Exam #2 Summer 2007 ON THE FRONT OF YOUR BLUEBOOK write: (1} your name, (2) your student ID number, (3) APPM 1360, and (4) a grading table. You must work all of the problems on the exam. Show ALL of. your work in your bluebook and BOX IN YOUR FINAL ANSWERS. A correct answer with no relevant work may receive no credit, while an incorrect answer accompanied by some correct work may receive partial credit. Text books, class notes, calculators, and electronics of any kind are NOT permitted. 1. (20 points} True or False: if the statement is always true, put True (not just T); if the statement is not always true, put False (rot just F). dx a defined to be 1 (a) i+ +e is defined to “tal me False: = where ¢ is any fixed number. anne g x (b) If a,,,2a, forall, and g, is bounded below, then lima, exists. False: If a, increases it must be bounded above; if it decreases it must be bounded below. J dx fi 4 (c) J tin(y? converges for p>I. 2 1 o False: Let u=In(x), then the integral becomes J sau=f taut si du, and the o # o 14 1 integral foau diverges. ou {4 . (d) J oF converges. oe e 0 1 False: Let u=x—2, then cS gol aI wy fS+ . 9 m1 Ht x and the integrals wo, with limits at 0 diverge.