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Unformatted text preview: MATH 1241 Common Final Exam Fall 2010 Please print the following information: Name: Instructor: Student ID: Section/Time: The MATH 1241 Final Exam consists of three parts. You have three hours for the entire test. But you have only one hour to complete the first part. You must turn in Part I at 9:00 a.m. You can start working on Part II or Part III as soon as you finish working with Part I, however you are not allowed to use calculators until 9:00 a.m. These pages contain Part I which consists of 15 multiple choice questions. A special answer sheet is provided so that your answers can be machine graded. 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. However if you mark more than one answer to a question, that 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 the end of the examination you MUST hand in this booklet, your answer sheet and all scratch paper. 1 Part I (CALCULATORS ARE NOT ALLOWED) . 1. The derivative of f ( x ) = x 2 + x 1 (a) is equal to 2 x (b) is equal to 2 x 1 (c) is equal to 2 x + 1 (d) is equal to x + 1 (e) is equal to x 2 + x 2. The derivative of f ( x ) = 1 x 9 (a) is equal to 9 /x 9 (b) is equal to 1 /x 10 (c) is equal to 9 /x 10 (d) is equal to 9 /x 10 (e) is equal to 1 / (9 x 8 ) 3. The limit lim x x 2 x 4 + 1 (a) is equal to 2 (b) is equal to 5 (c) is equal to 1 (d) is equal to (e) is equal to 0 2 4. Find the value of the parameter b for which the function f ( x ) = ( x, if x < 1 , 2 x + b, if x 1 . is continuous on the interval ( , ) (a) b = 3 (b) b = 3 (c) b = 1 (d) b = 0 (e) b = 1 5. The equation of the tangent line to the graph of the function f ( x ) = e 2 x 1 at the point with coordinates x = 0, y = 0 (a) is y = 2 x + 1 (b) is y = 2 x (c) is y = 7 x (d) is y = 9 x (e) is y = 2 x 6. The derivative of the function f ( x ) = ln(1 + x 8 ) equals (a) 8 x 7 1 + x 8 (b) 1 1 + 8 x 7 (c) x 7 1 + x 8 (d) 1 1 + x 8 (e) ln(8 x 7 ) 3 7. According to LHospitals rule, the limit lim x ln(1 + 4 x ) 2 x (a) is equal to 3 (b) is equal to 1 (c) is equal to 5 (d) is equal to (e) is equal to 2 8. The derivative of the function f ( x ) = e x cos( x ) equals (a) e x (cos( x ) sin( x )) (b) e x sin( x ) (c) e x cos( x ) (d) e x (sin( x ) + cos( x )) (e) 2 sin( x ) + 2 cos( x ) 9. The derivative of the function f ( x ) = x 2 + 2 x + 5 equals (a) f ( x ) = 2 x + 2 (b) f ( x ) = x +1 x 2 +2 x +5 (c) f ( x ) = 2 x + 2 (d) f ( x ) = 2 x +2 x 2 +2 x +5 (e) f ( x ) = x 2 4 10.10....
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 Spring '08
 XIU
 Math

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