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Unformatted text preview: Millersville University Name Department of Mathematics MATH 211, Calculus II , Final Examination May 10, 2007, 2:45PM4:45PM Please answer the following questions. Your answers will be evaluated on their correctness, completeness, and use of mathematical concepts we have covered. Please show all work and write out your work neatly. Answers without supporting work will receive no credit. The point values of the problems are listed in parentheses. 1. (5 points) The region bounded by the graph of f ( x ) = sin x x , the xaxis, and the lines x = π/ 2 and x = π is revolved around the yaxis. Find the exact volume of the resulting solid of revolution. 2. (6 points each) Determine if the following infinite series are divergent, conditionally convergent, or absolutely convergent. You must justify your answers. (a) ∞ summationdisplay k =1 ( 1) k +1 1 1 + √ k (b) ∞ summationdisplay k =1 ( 2) k +1 k + 5 k (c) ∞ summationdisplay k =1 ( 1) k +1 10 k k 10 (d) ∞ summationdisplay k =2 1 k (ln k ) 2 3. (5 points) A spring has a natural length of 10 inches. A force of 800 pounds stretches3....
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This test prep was uploaded on 04/19/2008 for the course MATH 211 taught by Professor Buchanan during the Spring '07 term at Millersville.
 Spring '07
 buchanan
 Calculus

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