. Assume that f is an increasing, nonnegative function on [a, b]. What can be concluded about the relationships among LRAMn f, RRAMn f, and the are n [a, b]? . Assume that f is a decreasing, nonnegative function on [a, b]. What can always be concluded about the relationships among LRAMn f, RRAMn f, and he area on [a, b]? . Prove or disprove the following statement: MRAM, f is the average of LRAM f and RRAMn f. Give specific examples. . Given the function f(x) = 2x over the interval [0, 3], explain how to find a formula for the Riemann sum obtained by dividing the interval into n ubintervals and using the right-hand endpoint for each c;. Then take a limit of these sums as n approaches infinity to calculate the area under the curve ver the interval.

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I - RAM and Riemann Discussion
35 35
1. Assume that f is an increasing, nonnegative function on [a, b]. What can be concluded about the relationships among LRAMn f, RRAMn f, and the area
on [a, b]?
2. Assume that f is a decreasing, nonnegative function on [a, b]. What can always be concluded about the relationships among LRAMn f, RRAMn f, and
the area on [a, b]?
3. Prove or disprove the following statement: MRAMn f is the average of LRAMn f and RRAMn f. Give specific examples.
4. Given the function f(x) = 2x over the interval [0, 3], explain how to find a formula for the Riemann sum obtained by dividing the interval into n
subintervals and using the right-hand endpoint for each c₁. Then take a limit of these sums as n approaches infinity to calculate the area under the curve
over the interval.
Transcribed Image Text:I - RAM and Riemann Discussion 35 35 1. Assume that f is an increasing, nonnegative function on [a, b]. What can be concluded about the relationships among LRAMn f, RRAMn f, and the area on [a, b]? 2. Assume that f is a decreasing, nonnegative function on [a, b]. What can always be concluded about the relationships among LRAMn f, RRAMn f, and the area on [a, b]? 3. Prove or disprove the following statement: MRAMn f is the average of LRAMn f and RRAMn f. Give specific examples. 4. Given the function f(x) = 2x over the interval [0, 3], explain how to find a formula for the Riemann sum obtained by dividing the interval into n subintervals and using the right-hand endpoint for each c₁. Then take a limit of these sums as n approaches infinity to calculate the area under the curve over the interval.
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