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Unformatted text preview: The University of British Columbia Final Examination  December 17, 2008 Mathematics 102 Instructors (Sections) (Circle one) : Drs. L. Keshet (101 / 104), K. Gunn (102), R. Israel (103) I. Rozada (105), J. Allard (106) Closed book examination Time: 2.5 hours First Name : Family name: Student #: Signature Special Instructions: Be sure that this examination has 13 pages. The last page contains useful formulae Write your full name (as on your Student ID) on top of each page. You may use backs of pages for scrap work, (or extra space, if needed). No calculators, electronic devices, books, or notes are permitted. Unless otherwise indicated, show all your work. Answers not supported by calculations or rea soning may not receive credit. Messy work will not be graded. At the end of the examination period: 1. You will be instructed to put away all writing implements (Continuing to write past this signal is considered cheating). 2. Remain in your seats until exams have been collected. 3. You will be instructed when you are free to leave. Rules governing examinations • Each candidate should be prepared to produce her/his library/AMS card upon request. • No candidate shall be permitted to enter the exami nation room after the expiration of one half hour, or to leave during the first half hour of examination. • Candidates are not permitted to ask questions of the invigilators, except in cases of supposed errors or ambi guities in examination questions. • CAUTION  Candidates guilty of any of the follow ing or similar practices shall be immediately dismissed from the examination and shall be liable to disciplinary action. (a) Making use of any books, papers, or memoranda, other than those authorized by the examiners. (b) Speaking or communicating with other candidates. (c) Purposely exposing written papers to the view of other candidates. • Smoking is not permitted during examinations. 1 15 2 12 3 10 4 10 5 10 6 12 7 11 8 10 9 10 Total 100 Page 1 out of 13 December 2008 Math 102 Name: Page 2 out of 13 Problem 1: Multiple Choice Questions: Select ONE correct answer (a, b, c, d, or e) and write it in Table 1. You will not be graded for any work or answers outside those boxes. 1.1 : The equation of the tangent line to the function y = f ( x ) at the point x is (a) y = f ( x ) + f prime ( x )( x x ) (b) y = f prime ( x ) + f ( x )( x x ) (c) y = x + f ( x ) /f prime ( x ) (d) y = f ( x ) f prime ( x )( x x ) (e) y = f ( x ) f prime ( x )( x x ) 1.2 : The functions f ( x ) = x 2 and g ( x ) = x 3 are equal at x = 0 and at x = 1. Between x = 0 and x = 1, for what value of x are their graphs furthest apart?...
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 Winter '08
 LALALA
 Math, Personal name, Family name, Given name

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