vide the interval into n subintervals of equal length. How long is each subinterval? ength is ote: Your answer should be in terms of n. order to determine an overestimate for the area under the graph of the function, at what x- lue should you evaluate f(x) to determine the height of the first rectangle? valuate at ote: Your answer should be in terms of n. nd a formula for the x-value in the kth subinterval which determines the height of the kth ctangle. valuate at ote: Your answer should be in terms of k and n. rite down a Riemann sum for f(x) over the given interval which is guaranteed to be an erestimate. n emann sum is >. k=1 ote: Your answer should be in terms of k and n; there should be no other letters in your Iswer. п(n + 1) sing the formula >, k = write down the above Riemann sum without using a E. 2 k=1 emann sum is ote: Your answer should be in terms of n. ompute the limit of the above sum as n → ∞. ne limit is ote: Your answer should be a number.

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Consider the function f(x)=4x over the interval [0,5]. (am having trouble with this, please help!)

Divide the interval into n subintervals of equal length. How long is each subinterval?
Length is
Note: Your answer should be in terms of n.
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?
Evaluate at
Note: Your answer should be in terms of n.
Find a formula for the x-value in the kth subinterval which determines the height of the kth
rectangle.
Evaluate at
Note: Your answer should be in terms of k and n.
Write down a Riemann sum for f(x) over the given interval which is guaranteed to be an
overestimate.
Riemann sum is >,
k=1
Note: Your answer should be in terms of k and n; there should be no other letters in your
answer.
n
п(n + 1)
Using the formula >, k
write down the above Riemann sum without using a E.
2
k=1
Riemann sum is
Note: Your answer should be in terms of n.
Compute the limit of the above sum as n → ∞.
The limit is
Note: Your answer should be a number.
Transcribed Image Text:Divide the interval into n subintervals of equal length. How long is each subinterval? Length is Note: Your answer should be in terms of n. 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? Evaluate at Note: Your answer should be in terms of n. Find a formula for the x-value in the kth subinterval which determines the height of the kth rectangle. Evaluate at Note: Your answer should be in terms of k and n. Write down a Riemann sum for f(x) over the given interval which is guaranteed to be an overestimate. Riemann sum is >, k=1 Note: Your answer should be in terms of k and n; there should be no other letters in your answer. n п(n + 1) Using the formula >, k write down the above Riemann sum without using a E. 2 k=1 Riemann sum is Note: Your answer should be in terms of n. Compute the limit of the above sum as n → ∞. The limit is Note: Your answer should be a number.
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