Single Variable Calculus: Concepts and Contexts

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Your Name Section Number Your TA’s Name Section Time I agree to abide by the Honor Code. Signature Math 20 Winter 2000 Prof. Moore Final Exam Directions: You may use a graphing calculator to compute and graph things during the exam, but you may not use any notes or books, or receive help from any person. Show all of your work, explaining as much as possible. 1. a) (2 points) Fill in the blank (no explanation necessary): If a function is always , then the right endpoint approximation is an underestimate. b) (2 points) Fill in the blank (no explanation necessary): If a function is always , then the midpoint approximation is an underestimate. c) (6 points) Use the trapezoidal approximation to estimate 1 0 e x 2 dx , splitting the interval into three equal-sized pieces. Show as much work as possible and give your answer as an approximation to 4 decimal places.
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2. A region A is bounded by y = x and the x -axis for the values 0 x 4, and is rotated about the line x = 5 to obtain a solid.
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