M160 Suggested Concept Quiz on Riemann Sums/Definite …
MATH 160 Concept Quiz Name: ______________________________
Date due: Friday, April 11, 2008 MATH 160 sec. ____8___
Time Limit: None – take home! Calculator: REQUIRED References: Recommend using no references
1. 1. The graph of the function f(x) = x2 – 2x on the interval [ 0, 3 ]is shown at right.
Partition the interval [ 0, 3] on the x-axis into subintervals of length [pic]
Mark the partition points and label them x0, x1, x2, etc.
2. Choose evaluation points that could be used to calculate a Riemann sum for the function f(x) = x2 – 2x based on the partition of [0, 3] you created in #1. Clearly list these evaluation points in the space below. Mark the evaluation points in the figure and label them c1, c2, c3, etc.
[pic]
3. Write an expression in expanded form (i.e. not using sigma notation) for the specific Riemann sum for the function f(x) = x2 – 2x formed by using the partition and evaluation points you chose in #1 and #2.
Calculate the exact numerical value of this Riemann sum. (Use your calculator. Do not round your answer.)
4. Illustrate in the figure (draw!) and explain (write about what you drew!) how to interpret the Riemann sum you wrote in #3 graphically.
5. (a) How would you choose a partitioning { x0, x1, x2,…, xn } of [ 0, 3] so that no matter where the evaluation points { c1, c2, c3,…, cn } are located the Riemann sum computed from this partitioning of [ 0, 3] will be very close to the exact numerical value of [pic]?
(b) Explain how to see that all the Riemann sums computed using a partitioning of [0, 3] chosen in the way you described in (a) will be very close to the exact numerical value of [pic].
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