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MTH132-Quiz6

# MTH132-Quiz6 - ∆ ⋅ n k k k x c f 1 Usually we choose...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: 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 (b) = 4 1 cos k k π 2. Evaluate the sums by formulas. (a)[2 pts] = - 7 2 ) 2 ( k k (b)[3 pts] = + 5 1 ) 5 3 ( 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) = 4 4 ) ( dx x g

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Page 2 10/18/2011 (b) = 2 5 ) ( dx x f (c) = - 5 1 )] ( 3 ) ( 5 [ dx x g x f 4. Let 1 2 ) ( + = x x f defined over ] 3 , 0 [ . Consider the Riemann sum: =
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Unformatted text preview: ∆ ⋅ n k k k x c f 1 ) ( . Usually, we choose equal length n a b x x k / ) (-= ∆ = ∆ . (a) [2 pts]. Partition ] 3 , [ into 4 subintervals of equal length, then choose the right-hand endpoint of each subinterval ( x k a x c k k ∆ + = = ) to evaluate the Riemann sum. (b) [2 pts]. Find a formula for the Riemann sum obtained by dividing the interval into n equal subintervals. (c) [1 pt]. Find a definite integral to express the limit of the Riemann sum as n approaches infinity. (d) [bonus 2 pts]. Evaluate this definite integral. (Take the limit of this sum or use the area of a certain region)...
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MTH132-Quiz6 - ∆ ⋅ n k k k x c f 1 Usually we choose...

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