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MTH132-Quiz6-Solutions (1) - Page 1 Name(Print Clearly...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: MTH132 Section 5 & 18, Quiz 6 Nov 17, 2008 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 15 minutes. 1. [2 pts each] . Convert the sigma notations to addition (summation) notation and evaluate the sums. (a) = + 2 1 1 6 k k k 7 4 3 1 2 2 6 1 1 1 6 = + = + + + (b) = 4 1 cos k k π 0 1 1 1 1 4 cos 3 cos 2 cos cos = + - + - = + + + π π π π 2. Evaluate the sums by formulas. (a)[2 pts] 54 27 2 ) 1 28 ( 2 ) 1 2 ) 1 7 ( 7 ( 2 ) 1 ( 2 ) 2 ( 7 1 7 2 - = × - = - × - = - + × - = - - = - = = k k k k (b)[3 pts] 240 75 165 2 6 5 5 6 11 6 5 3 5 3 ) 5 3 ( ) 5 3 ( 5 1 5 1 2 5 1 2 5 1 = + = × + × × = + = + = + = = = = k k k k k k k k k k 3. [2 pts each]. Suppose 4 ) ( 2 1 - = dx x f , 6 ) ( 5 1 = dx x f , 8 ) ( 5 1 = dx x g . Use the rules to find (a) 0 ) ( 4 4 = dx x g (b) 10 )) 4 ( 6 ( ) ) ( ) ( ( ) ( ) ( 5 2 5 1 2 1 2 5 - = - - - = - - = - = dx x f dx x f dx x f dx x f (c) = - = × - × = - = - 5 1 5 1 5 1 6 24 30 8 3 6 5 ) ( 3 ) ( 5 )] ( 3 ) ( 5 [ dx x g dx x f dx x g x f
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Page 2 10/18/2011 4. Let 1 2 ) ( + = x x f defined over
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