Let f(x) = x³, and compute the Riemann sum of f over the interval [2, 3], choosing the representative points to be the midpoints of the subintervals and usingthe following number of subintervals (n). (Round your answers to two decimal places.)(a) Two subintervals of equal length (n 2)(b) Five subintervals of equal length (n = 5)(c) Ten subintervals of equal length (n = 10)(d) Can you guess at the area of the region under the graph of f on the interval [2, 3]?square units

The given function is The midpoint rule

Answered: Let f(x) = x³, and compute the Riemann…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
1. Let f(x) = x3 and compute the Riemann sum of f over the interval [1,2], using the following number of subintervals (n). In each case, choose the representative points to be the left endpoints of the subintervals. (Round your answers to two decimal places.) (a) Use two subintervals of equal length (n = 2). (b) Use five subintervals of equal length (n = 5). (c) Use ten subintervals of equal length (n = 10). (d) Can you guess at the area of the region under the graph of f on the interval [1, 2]? square units 2. Let f(x) = x3, and compute the Riemann sum of f over the interval [8, 9], choosing the representative points to be the right endpoints of the subintervals and using the following number of subintervals (n). (Round your answers to two decimal places.) (a) two subintervals of equal length (n = 2) b) five subintervals of equal length (n = 5) (c) ten subintervals of equal length (n = 10) (d) Can you guess at the area of the region under the graph of f on the…
Let f(x) = 4x with the interval [0, 2]. (a) Use a Riemann sum with four subintervals of equal length (n = 4) to approximate the area of R. Choose the representative points to be the right endpoints of the subintervals. (b) Repeat part (b) with eight subintervals of equal length (n = 8).
Let f(x) = x2, and compute the Riemann sum of f over the interval [8, 10], choosing the representative points to be the midpoints of the subintervals and using the following number of subintervals (n). (Round your answers to two decimal places.) (n = 2) (n = 5) (n = 10) Can you guess at the area of the region under the graph of f on the interval [8, 10]?
Let f(x) = x3, and compute the Riemann sum of f over the interval [8, 9], choosing the representative points to be the right endpoints of the subintervals and using the following number of subintervals (n). (Round your answers to two decimal places.) (n=2) (n=5) (n=10) Can you guess at the area of the region under the graph of f on the interval [8, 9]?
Let f(x)=x^2 and compute the Riemann sum of f over the interval [2,4], choosing the representative points to be the midpoints of the subintervals and using: a. Two subintervals of equal length (n=2) b. Five subintervals of equal length (n=5) c. Ten subintervals of equal length (n=10) d. Can you guess at the area of the region under the graph of f on the interval [2,4]?
Let f(x) = x3, and compute the Riemann sum of f over the interval [3, 4], choosing the representative points to be the right endpoints of the subintervals and using the following number of subintervals (n). (Round your answers to two decimal places.)
1. Let f(x) = x2, and compute the Riemann sum of f over the interval [7, 9], choosing the representative points to be the left endpoints of the subintervals and using the following number of subintervals (n). (Round your answers to two decimal places.) (a) Two subintervals of equal length (n = 2)(b) Five subintervals of equal length (n = 5)(c) Ten subintervals of equal length (n = 10)(d) Can you guess at the area of the region under the graph of f on the interval [7, 9]?square units
Let f(x) = x3, and compute the Riemann sum of f over the interval [5, 6], choosing the representative points to be the right endpoints of the subintervals and using the following number of subintervals (n). (Round your answers to two decimal places.) (a) Two subintervals of equal length (n = 2)(b) Five subintervals of equal length (n = 5)(c) Ten subintervals of equal length (n = 10)(d) Can you guess at the area of the region under the graph of f on the interval [5, 6]? What are the square units?
Let f(x)= 2x on the interval [0,4] Use a Riemann sum with four subintervals of equal length (n=4) to approximate the area of R. Choose the representative points to be the left endpoints of the subintervals.
Let f(x) = x3 and compute the Riemann sum of f over the interval [4,5], using the following number of subintervals (n). In each case, choose the representative points to be the left endpoints of the subintervals. (Round your answers to two decimal places.) (a) Use two subintervals of equal length (n = 2). (b) Use five subintervals of equal length (n = 5). (c) Use ten subintervals of equal length (n = 10). (d) Can you guess at the area of the region under the graph of f on the interval [4, 5]? square units
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