MA_125_Final_Exam-1 - Instructor Name Final Exam Calculus I...

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Instructor: Name: Final Exam Calculus I; Fall 2007 Part I Part I consists of 8 questions, each worth 5 points. Clearly show your work for each of the problems listed. In 1-3, find y 0 if: (1) y = x 2 - 1 x 2 +1 , (2) y = x ln( x 2 + 1), (3) y = 5 p cos( x ). 1
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(4) Find the equation of the tangent line to the graph of the func- tion y = f ( x ) = x at x = 4, (5) If the position at time t is given by S ( t ) = sin(5 t ), find the acceleration as a function of t . (6) Find the most general anti-derivative of the function y = f ( x ) = (7 x + 3) 21 .
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(7) Evaluate the limit lim x 0 x - sin( x ) x 3 (8) Use calculus to find two positive numbers whose sum is 100 and whose product is maximal.
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Part II Part II consists of 6 problems; the number of points for each part are indicated by [x pts]. You must show the relevant steps (as we did in class) and justify your answer to earn credit. Simplify your answer when possible. (1) [9 pts] Find the absolute maximum value and the absolute minimum value of the function f ( x ) = x 3 - 3 x 2 + 9 on the interval [ - 1 , 3].
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