Consider the function f(x) = 6x + 7x² over the interval 0, 1]. Divide the interval into n subintervals of equal length. How long is each subinterval? Length is In order to determine an overestimate for the area under the graph of the function, at what x-value should you evaluate f(x) to determine the height of the first rectangle? x = Find a formula for the x-value in the kth subinterval which determines the height of the kth rectangle. Write down a Riemann sum for f(x) over the given interval using the x-values you calculated above. Riemann sum is п(п + 1) and п(п + 1)(2n + 1) Using the formulas k = write down the above Riemann sum without using a E. 2 k=1 k=1 Riemann sum is (6n+7)(n+1)(2n+1)/(6n^2) Compute the limit of the above sum as n – 0.
Consider the function f(x) = 6x + 7x² over the interval 0, 1]. Divide the interval into n subintervals of equal length. How long is each subinterval? Length is In order to determine an overestimate for the area under the graph of the function, at what x-value should you evaluate f(x) to determine the height of the first rectangle? x = Find a formula for the x-value in the kth subinterval which determines the height of the kth rectangle. Write down a Riemann sum for f(x) over the given interval using the x-values you calculated above. Riemann sum is п(п + 1) and п(п + 1)(2n + 1) Using the formulas k = write down the above Riemann sum without using a E. 2 k=1 k=1 Riemann sum is (6n+7)(n+1)(2n+1)/(6n^2) Compute the limit of the above sum as n – 0.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.7: A Library Of Parent Functions
Problem 47E
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Transcribed Image Text:Consider the function f(x)
= 6x + 7x? over the interval 0, 1.
Divide the interval into n subintervals of equal length. How long is each subinterval?
Length is
In order to determine an overestimate for the area under the graph of the function, at what x-value should you evaluate f(x) to determine the height
of the first rectangle?
x =
Find a formula for the x-value in the kth subinterval which determines the height of the kth rectangle.
Write down a Riemann sum for f(x) over the given interval using the x-values you calculated above.
n
Riemann sum is )
k=1
п(п + 1)
п(п + 1)(2n +1)
n
Using the formulas ) `k
and ) k?
write down the above Riemann sum without using a E.
k=1
k=1
Riemann sum is (6n+7)(n+1)(2n+1)/(6n^2)
Compute the limit of the above sum as n → 0.
The limit is
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