University of Hawaii, Manoa - MATH 242IMG_265 DETAILED ANSWERS TO EXAM ( ANSWER KEY )

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Math 242 Midterm 2, Part II Name: Please circle your section: Recitation 1 Thurs 10:30-11:20 TA - Ikenna Nometa Recitation 2 Thurs 1:30-2:20 TA - Ikenna Nometa Recitation 3 Thurs 10:30-11:20 TA -... Donald Lee Recitation 4 Thurs 12-12:50 TA - Donald Lee Recitation 5 Fri 11:30-12:20 TA - Lance Ferrer Recitation 6 Fri 2:30-3:20 TA - Lance Ferrer Recitation 7 Fri 8:30-9:20 TA - Ryan Sasaki Recitation 8 Fri 9:30-10:20 TA - Ryan Sasaki Recitation 9 Fri 10:30-11:20 TA - Dan Flores Recitation 10 Fri 1:30-2:20 TA - Umar Gaffar Recitation 11 Thurs 8:00-8:50 TA - Samantha Pilgrim Recitation 12 Thurs 9:00-9:50 TA - Matt Lorentz Question Points Score 1 10 2 10 3 10 4 10 Total: 40 • You may use notes, the textbook, or the lectures posted on Laulima. • You may not use any electronic devices, other than to view the ebook version of the textbook, or the lectures on Laulima. • You must show all your work and make clear what your final solution is (e.g. by drawing a box around it). As you have a good amount of time to do this exam, you should give well-explained solutions. You are encouraged to do a rough solution on scratch paper, and write up a careful solution on the exam itself. • All work must be your own. By signing here, I confirm that I have followed all of the rules above. In particular, the work here is all my own. Signtaure: Date: Good luck! :)1. (10 points) Evaluate the integral. Be sure to indicate if the integral is improper. Z x(x22x++ 4 x + 1)dx Page 22. (10 points) Evaluate the integral. Be sure to indicate if the integral is improper. Z13(3 − x)−1=3dx Page 33. Suppose we want to use the n-term trapezoidal rule to approximate Z12 ln(x) dx (a) (3 points) Make a graph of ln(x) between x = 1 and x = 2. Draw on your graph the trapezoids used to apply the trapezoidal rule with n = 3. (So, your graph should have 3 trapezoids.) (b) (2 points) Does the trapezoidal rule overestimate or underestimate the value of R12 ln(x)dx? You do not have to justify your answer. (c) (5 points) For the trapezoidal rule, the error to Rab f(x)dx can be estimated by En ≤ (b−12an)32M , where M is the maximum value of jf00(x)j over the interval [a; b]. Suppose you want to compute R12 ln(x)dx with tolerance 0:01. How big should you choose n? Page 44. For the following problems, determine if the series is absolutely convergent, conditionally convergent or divergent. Carefully justify each answer. (a) (5 points) 1 Xn =2 1 1 + (−2)n (b) (5 points) 1 Xn =2 (−1)n 1 1 + 2−n Page 5 [Show More]

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