exam 3 fall 2007 - Engineering Mathematics(E35 317 Exam 3...

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Engineering Mathematics (E35 317) Exam 3 November 7, 2007 This exam contains four multiple-choice problems worth two points each, twelve true-false problems worth one point each, and four free-response problems worth 20 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. Let , and observe that . Find the value of 0ÐBß Cß DÑ œ BC  D f0ÐBß Cß DÑ œ ÒC ß #BCß "Ó # # the following line integral. . ' Ð"ß#ß$Ñ Ð%ß&ß'Ñ # ÐC .B  #BC .C  .DÑ (A) ! (B) " (C) #" (D) #& (E) &% (F) &( (G) (# (H) (% (I) *$ (J) *& 2. The vector equation below is a parameterization of which of the following surfaces?r pÐ?ß @Ñ œ Ò@?ß @?ß @Ó! Ÿ ? Ÿ #! Ÿ @ Ÿ %cossin1 (A) circular cylinder(B) disk(C) cone(D) sphere(E) plane(F) none of the above
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3. Consider the following differential equation.Ð"  B ÑCC C œ !#www"BB#% Let . According to the applicable convergence theorem, any series in the solution is B œ ! ! guaranteed to converge at least on what interval?
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