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Unformatted text preview: MATH 2203 &Final Exam (Version 1) Solutions May 4, 2011 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathe- matical correctness and clarity of presentation . In other words, you must know what you are doing (mathematically) and you must also express yourself clearly. In particular, write answers to questions using correct notation and using complete sentences where appropriate. Also, you must supply su cient detail in your solutions (relevant calculations, written explanations of why you are doing these calculations, etc.). It is not su cient to just write down an &answerwith no explanation of how you arrived at that answer. As a rule of thumb, the harder that I have to work to interpret what you are trying to say, the less credit you will get. You may use your calculator but you may not use any books or notes. 1. Evaluate Z C ( x + y ) ds where C is the straight line segment joining the point (0 ; 1) to the point (1 ; 0) . Solution: The line segment can be parameterized by r ( t ) = t i + (1 & t ) j , t 1 . From this we obtain r ( t ) = i & j and j r ( t ) j = p 2 . Therefore Z C ( x + y ) ds = p 2 Z 1 (1) dt = p 2 ....
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