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Unformatted text preview: 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 13, find y if: (1) y = x 2 1 x 2 +1 , (2) y = x ln( x 2 + 1), (3) y = 5 p cos( x ). 1 (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 antiderivative of the function y = f ( x ) = (7 x + 3) 21 . (7) Evaluate the limit lim x x sin( x ) x 3 (8) Use calculus to find two positive numbers whose sum is 100 and whose product is maximal. 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....
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 Fall '07
 Department
 Calculus

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