exam 3 spring 2008 - Engineering Mathematics(ESE 317 Exam 3...

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Engineering Mathematics (ESE 317) Exam 3 April 2, 2008 This exam contains eight multiple-choice problems worth two points each, seven true-false problems worth one point each, and some free-response problems worth 17 points altogether, for an exam total of 40 points. Part I. Multiple-Choice Clearly circle the only correct response. Each is worth two points. 1. What type of surface is represented by the following vector equation?r pÐ?ß @Ñ œ Ò#@?ß #@?ß @Ó! Ÿ ? Ÿ! Ÿ @ Ÿ "cossin1 (A) circular cylinder(B) half of a circular cylinder(C) disk(D) half of a disk(E) cone(F) half of a cone(G) sphere(H) half of a sphere 2. What information can be obtained from the pull-off terms which result from the following equation? (Your answer should include the information obtained from them — no exactly more and no less.) ! ! ! 7œ! 7œ! 7œ! _ _ _ 7 7 7 7" 7" 7$ Ð7  #ÑÐ7  "Ñ+ B Ð7  #Ñ+ B + B œ ! (A) no information can be obtained from the pull-off terms (B) + œ ! ! (C) + œ ! " (D) and + œ ! + œ ! ! 1 (E) + œ + " ! (F) + œ  + " ! # $ (G) + œ  + " ! " $ (H) + œ + " ! " $ (I) + œ + " ! # $ (J) + œ + " !
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3. Consider the following differential equation, and let . According to the applicable B œ ! ! convergence theorem, all series in the solutions of this differential equation converge at least on what interval? ÐB  #ÑC  ÐB  "ÑC  BC œ ! ww w (A) Ð%ß %Ñ (B) Ð#ß #Ñ (C) Ð"ß "Ñ (D) Ð!ß "Ñ (E) Ð!ß #Ñ (F) Ð!ß %Ñ (G) Ð!ß _Ñ (H) Ð"ß _Ñ (I) Ð#ß _Ñ (J) Ð%ß _Ñ
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