This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 115 First Midterm October 12, 2010 Name: EXAM SOLUTIONS Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 10 pages including this cover. There are 8 problems. Note that the problems are not of equal difficulty, so you may want to skip over and return to a problem on which you are stuck. 3. Do not separate the pages of this exam. If they do become separated, write your name on every page and point this out to your instructor when you hand in the exam. 4. Please read the instructions for each individual problem carefully. One of the skills being tested on this exam is your ability to interpret mathematical questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work (including appropriate explanation) for each problem, so that graders can see not only your answer but how you obtained it. Include units in your answer where that is appropriate. 6. You may use any calculator except a TI92 (or other calculator with a full alphanumeric keypad). However, you must show work for any calculation which we have learned how to do in this course. You are also allowed two sides of a 3 00 5 00 note card. 7. If you use graphs or tables to find an answer, be sure to include an explanation and sketch of the graph, and to write out the entries of the table that you use. 8. Turn off all cell phones and pagers , and remove all headphones. Problem Points Score 1 15 2 12 3 10 4 10 5 10 6 11 7 14 8 18 Total 100 Math 115 / Exam 1 (October 12, 2010) page 2 1 . [15 points] The following figure shows the graph of y = f ( x ) for some function f . The dotted line signifies a vertical asymptote. 4 2 2 4 6 x 1 1 2 3 4 5 y a . [12 points] Using the graph, give the values of each of the following quantities if they exist. Choose your answer in each part from the numbers 0 , 1 , 2 , 3 or the words Does not exist. Answers may be used more than onceor not at all. i) f (1) = Does not exist. ii) f (2) = 1 iii) f (3) = Does not exist. iv) f ( 1) = . v) f (1) = Does not exist. vi) f (2) = Does not exist. vii) lim x + f ( x ) = . viii) lim x 3 f ( x ) = Does not exist. ix) lim x 2 f ( x ) = 1 . x) lim x 1 f ( x ) = 3 . xi) lim x  1 f ( x ) = 1 . xii) lim x  f ( x ) = Does not exist. b . [3 points] Still looking at the graph, is f continuous at the following x values? (Yes or No) i) x = 1 , No. ii) x = 2 , Yes. iii) x = 3 , No. Math 115 / Exam 1 (October 12, 2010) page 3 2 . [12 points] A continuous (but not necessarily differentiable) function, f , defined for all real numbers has the following properties: a. f ( x ) = 1 for x < 1 b. f is concave up for 1 < x < 3 c. f (2) = 1 d. f (2) = 0 e. lim x + f ( x ) = 2 f. f 00 ( x ) > 0 for x > 5 On the axes below, draw a possible sketch of y = f ( x ) including labels where appropriate....
View
Full
Document
This note was uploaded on 01/28/2012 for the course MATH 115 taught by Professor Blakelock during the Fall '08 term at University of Michigan.
 Fall '08
 BLAKELOCK
 Math

Click to edit the document details