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Unformatted text preview: Makeup Final Exam, Math 240: Calculus III September, 2011 No books, papers or may be used, other than a handwritten note sheet at most 8 . 5 00 × 11 00 in size. All electronic devices must be switched off during the exam. This examination consists of nine (9) long answer questions and one (1) true/false question. Partial credits will be given only when a substantial part of a long answer question has been worked out. Merely displaying some formulas is not sufficient ground for receiving partial credits. • Your name, printed: • Your Penn ID (last 4 of the middle 8 digits): My signature below certifies that I have complied with the University of Pennsylvania’s code of academic integrity in completing this examination. Your signature 1 2 3 4 5 6 7 8 9 10 Total Name: 1 1. For what values of k is the following matrix singular? 2 3 1 2 k k 6 4 Ans. k = . Name: 2 2. Consider the following differential equation x (1 x ) d 2 dx 2 + (3 4 x ) d dx 2 u ( x ) = 0 . (a) Find a real number μ such that there exists a solution of the form u ( x ) = x μ · 1 + X n ≥ 1 a n x n !...
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This note was uploaded on 03/06/2012 for the course MATH 240 taught by Professor Storm during the Fall '08 term at UPenn.
 Fall '08
 Storm
 Calculus

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