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Unformatted text preview: MATH 1241 COMMON FINAL EXAM SPRING 2006 1 PART I Name: Instructor: Student ID #: Section/Time: This exam is divided into three parts. Calculators are not allowed on Part I. You have three hours for the entire test, but you have only one hour to finish Part I. You must turn in the answer sheet for Part I at 9:00 am. You may start working on the other two parts of the exam whenever you are done with Part I, but you cannot use your calculator until ALL of the Part I answer sheets are collected. After these answer sheets are collected, your instructor will announce that calculators are allowed on Parts II and III. These pages contain Part I which consists of 12 multiple choice questions. These questions must be answered without the use of a calculator. • You must use a pencil with a soft black lead (# 2 or HB) to enter your answers on the answer sheet. • For each question choose the response which best fits the question. • If you wish to change an answer, make sure that you completely erase your old answer and any other extraneous marks. • There is no penalty for guessing. • If you mark more than one answer to a question, the question will be scored as incorrect. • You may perform your calculations on the test itself or on scratch paper, but do not make any stray marks on the answer sheet. • Make sure that your name appears on the answer sheet and that you fill in the circles corresponding to your name. At approximately 9:00 am, you MUST hand in the answer sheet for Part I. At the end of the exam, you MUST hand in all remaining test materials including test booklets, answer sheet for Part II, and scratch paper. MATH 1241 COMMON FINAL EXAM SPRING 2006 2 1. If h ( x ) = ln( x + 3), then the inverse of h ( x ) is (a) h 1 ( x ) = e x 3 (b) h 1 ( x ) = e x 3 (c) h 1 ( x ) = e x +3 (d) h 1 ( x ) = 1 x + 3 (e) h ( x ) does not have an inverse since it is not onetoone on its domain ( 3 , ∞ ). 2. The first graph below is the graph of y = f ( x ). Which of the graphs labeled (a), (b), (c), (d) and (e) best represents the graph of y = f ( x 2) + 1? y x 2 1 1 2 2 2 0 y=f(x) Graph of y = f ( x ) 2 y x 1 1 0 2 2 4 (a) y x 1 4 2 0 1 2 3 (b) y x 1 1 0 2 2 2 4 (c) y x 1 1 2 3 0 4 2 (d) y x 1 2 3 4 2 0 1 (e) MATH 1241 COMMON FINAL EXAM SPRING 2006 3 3. lim x → 1 x 2 + 2 x 3 2 x 2 2 = (a) 0 (b) 1 2 (c) 1 (d) 3 2 (e) Does not exist. 4. lim x →∞ x 2 + 2 x 3 2 x 2 2 = (a) 0 (b) 1 2 (c) 1 (d) 3 2 (e) Does not exist. 5. Let f ( x ) = sin(2 x ) x , x = 0 , k, x = 0 , where k is a constant. Determine the value of k that makes f continuous at x = 0. (a) 0 (b) 1 2 (c) 1 (d) 2 (e) No value of k makes f continuous at x = 0. MATH 1241 COMMON FINAL EXAM SPRING 2006 4 6. Let f ( x ) = ln( x 2 3). Find f (2)....
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 Spring '08
 XIU
 Math, Derivative, Continuous function, Convex function, Concave function, Common Final Exam

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