Exam #2 APPM1360 Spring 2007 ON THE FRONT OF YOUR BLUEBOOK write: (1) your name, (2) your student ID number, (3) lecture section (4) your instructor’s name, and (5) 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 answer. 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, and calculators are NOT permitted. Maximum score: 115 points. Question 1 : 16 points, Question 2 : 18 points, Question 3 : 24 points, Question 4 : 24 points, Question 5 : 10 points, Question 6 : 18 points 1. Evaluate the following: ( a ) Z 1 x 2 √ x 2-1 d x , ( b ) ∞ X n = 1 ﬂ cos n n 2-cos ( n + 1 ) ( n + 1 ) 2 ± 2. (a) Determine if the integral Z ∞-∞ 1 + x 1 + x 2 d x converges or diverges. (b) Calculate lim t → ∞ Z t-t 1 + x 1 + x 2 d x . (c) Is the result in part (b) consistent with your answer in part (a)? Explain.
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