Definition: The AREAA of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles A = lim R, = lim [f(x1)Ax + f(T2)Ar+… +f(xn)A¤] ... n+00 n00 |vspacelin (a) Use the above Definition to determine which of the following expressions represents the area under the graph of f(x) = x³ from a = 0 to x = 1. 1 А. lim n-00 n 3 В. lim n+00 n С. lim n-00 n n D. lim (b) Evaluate the limit that is the correct answer to part (a). You may find the following formula for the sum of cubes helpful: 13 + 23 + 33+...+n³ п(п + 1) Value of limit =
Definition: The AREAA of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles A = lim R, = lim [f(x1)Ax + f(T2)Ar+… +f(xn)A¤] ... n+00 n00 |vspacelin (a) Use the above Definition to determine which of the following expressions represents the area under the graph of f(x) = x³ from a = 0 to x = 1. 1 А. lim n-00 n 3 В. lim n+00 n С. lim n-00 n n D. lim (b) Evaluate the limit that is the correct answer to part (a). You may find the following formula for the sum of cubes helpful: 13 + 23 + 33+...+n³ п(п + 1) Value of limit =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 57E
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I don't know how to solve the attached Reiman sum question.
![Definition: The AREAA of the region S that lies under the graph of the continuous function
f is the limit of the sum of the areas of approximating rectangles
A = lim R, = lim [f(x1)Ax + f(T2)Ar+… +f(xn)A¤]
...
n+00
n00
|vspacelin
(a) Use the above Definition to determine which of the following expressions represents
the area under the graph of f(x) = x³ from a = 0 to x = 1.
1
А. lim
n-00
n
3
В. lim
С. lim
n-00
n
n
D. lim
n-00
n.
(b) Evaluate the limit that is the correct answer to part (a). You may find the following
formula for the sum of cubes helpful:
13 + 23 + 33+...+n³
п(п + 1)
2
Value of limit =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3cfeff4-8ba6-46a8-98d4-804b4f4f620a%2Fde732d8e-2c0d-4a73-9de6-135db6dc3014%2Fg64lqgr_processed.png&w=3840&q=75)
Transcribed Image Text:Definition: The AREAA of the region S that lies under the graph of the continuous function
f is the limit of the sum of the areas of approximating rectangles
A = lim R, = lim [f(x1)Ax + f(T2)Ar+… +f(xn)A¤]
...
n+00
n00
|vspacelin
(a) Use the above Definition to determine which of the following expressions represents
the area under the graph of f(x) = x³ from a = 0 to x = 1.
1
А. lim
n-00
n
3
В. lim
С. lim
n-00
n
n
D. lim
n-00
n.
(b) Evaluate the limit that is the correct answer to part (a). You may find the following
formula for the sum of cubes helpful:
13 + 23 + 33+...+n³
п(п + 1)
2
Value of limit =
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