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Unformatted text preview: M ATH 115 F IRST M IDTERM E XAM October 10, 2006 NAME: SOLUTIONS INSTRUCTOR: SECTION NUMBER: 1. Do not open this exam until you are told to begin. 2. This exam has 10 pages including this cover. There are 9 questions. 3. Do not separate the pages of the exam. If any pages do become separated, write your name on them and point them out to your instructor when you turn in the exam. 4. Please read the instructions for each individual exercise carefully. One of the skills being tested on this exam is your ability to interpret questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work for each exercise so that the graders can see not only the answer but also how you obtained it. Include units in your answers where appropriate. 6. You may use your calculator. You are also allowed two sides of a 3 by 5 notecard. 7. If you use graphs or tables to obtain an answer, be certain to provide an explanation and sketch of the graph to show how you arrived at your solution. 8. Please turn off all cell phones and pagers and remove all headphones. PROBLEM POINTS SCORE 1 9 2 12 3 12 4 10 5 8 6 12 7 11 8 12 9 14 TOTAL 100 2 1. (3 points each. No partial credit.) The questions on this page are multiple choice. They do not require an explanation. For each question, circle your choice for the correct answer(s). There may be more than one correct choice. Circle ALL answers that must be true about the given statement. (a) The function h ( x ) = x 5 x 3 + 2 x 2 x 3 3 x 2 (i) is undefined for x = 0 and x = 3 . (ii) has a horizontal asymptote of y = 2 / 3 . (iii) has vertical asymptotes at x = 0 and x = 3 . (iv) approaches as x approaches . (v) has a horizontal asymptote of y = 1 . (b) If a function f is continuous at x = a , then (i) lim x a f ( x ) exists. (ii) lim x a f ( x ) = f ( a ) . (iii) lim x a f ( x ) = f ( a ) . (iv) f is differentiable at x = a . (v) none of (i)(iv) must be true. (c) If lim x 3 g ( x ) = 5 for some function g , then (i) g (3) = 5 . (ii) g is continuous at x = 3 . (iii) lim x 3 g ( x ) = lim x 3 + g ( x ) . (iv) g (3) = 5 . (v) g is differentiable at x = 3 . 3 2. Suppose A ( t ) is a function that gives the average high temperature (in o F ) in Ann Arbor as a function of t measured in months where t = 0 represents January (the coldest month in Ann Arbor). (a) (2 points) Puerto Montt, a city in Chile, is approximately the same distance from the equator as Ann Arbor, but it is in the southern hemisphere where the warmest month is January....
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This note was uploaded on 04/02/2008 for the course MATH 115 taught by Professor Blakelock during the Fall '08 term at University of Michigan.
 Fall '08
 BLAKELOCK
 Calculus

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