Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 14E
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(Question 37 and 39)
Transcribed Image Text:37.
a. c.
YA
8
6
2
2
d. 20
y = 2x + 1
3
X
b. Δæ = 1; 0, 1, 2, 3, 4
(f
![37-42. Midpoint Riemann sums Complete the following steps for the given
function, interval, and value of n.
a. Sketch the graph of the function on the given interval.
b. Calculate Ax and the grid points x0, x1, ..., xn.
c. Illustrate the midpoint Riemann sum by sketching the appropriate
rectangles.
d. Calculate the midpoint Riemann sum.
37. f(x) = 2x + 1 on [0, 4]; n = 4
-1
38. f(x) = 2 cos ¹x on [0, 1]; n = 5
T
T
39. f(x)=√x on [1, 3]; n = 4
40. f(x) = x² on [0, 4]; n = 4
1
41. f(x):
on [1, 6]; n = 5
X
42. f(x) = 4 - x on [-1, 4]; n = 5
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F627ffe10-a730-4e4c-b7e9-b306478e5985%2Fbcfe7d48-aeb9-49a7-a501-3d38fa179a24%2Fmj5bkhe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:37-42. Midpoint Riemann sums Complete the following steps for the given
function, interval, and value of n.
a. Sketch the graph of the function on the given interval.
b. Calculate Ax and the grid points x0, x1, ..., xn.
c. Illustrate the midpoint Riemann sum by sketching the appropriate
rectangles.
d. Calculate the midpoint Riemann sum.
37. f(x) = 2x + 1 on [0, 4]; n = 4
-1
38. f(x) = 2 cos ¹x on [0, 1]; n = 5
T
T
39. f(x)=√x on [1, 3]; n = 4
40. f(x) = x² on [0, 4]; n = 4
1
41. f(x):
on [1, 6]; n = 5
X
42. f(x) = 4 - x on [-1, 4]; n = 5
=
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