*3. The following function is positive and negative on the given interval. f(x) = 9- x2; [0,4] a. Sketch the function on the given interval. b. Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n= 4. c. Use the sketch in part (a) to show which intervals of [0,4] make positive and negative contributions to the net area. a. Choose the correct answer below. O A. OB. Oc. D. Ay 18+ Ay 18+ AY 48- 12- Ay 18 12- 12- 12- 6- 6- 6- 0- 0+ 0- -6- -6- -6 -12- 42 48- -12- -12 -18 -18- -18- b. The net area, approximated using the left Riemann sum, is The net area, approximated using the right Riemann sum, is The net area, approximated using the midpoint Riemann sum, is c. Which intervals of [0,4] make positive and negative contributions to the net area? Choose the correct answer below. O A. Positive contributions on [2,4); negative contributions on [0,2] O B. Positive contributions on [0,3]; negative contributions on [3,4] O C. Positive contributions on [3,4]; negative contributions on [0,3] O D. Positive contributions on [0,2]; negative contributions on [2,4]
*3. The following function is positive and negative on the given interval. f(x) = 9- x2; [0,4] a. Sketch the function on the given interval. b. Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n= 4. c. Use the sketch in part (a) to show which intervals of [0,4] make positive and negative contributions to the net area. a. Choose the correct answer below. O A. OB. Oc. D. Ay 18+ Ay 18+ AY 48- 12- Ay 18 12- 12- 12- 6- 6- 6- 0- 0+ 0- -6- -6- -6 -12- 42 48- -12- -12 -18 -18- -18- b. The net area, approximated using the left Riemann sum, is The net area, approximated using the right Riemann sum, is The net area, approximated using the midpoint Riemann sum, is c. Which intervals of [0,4] make positive and negative contributions to the net area? Choose the correct answer below. O A. Positive contributions on [2,4); negative contributions on [0,2] O B. Positive contributions on [0,3]; negative contributions on [3,4] O C. Positive contributions on [3,4]; negative contributions on [0,3] O D. Positive contributions on [0,2]; negative contributions on [2,4]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![*3. The following function is positive and negative on the given interval.
f(x) = 9 – x²; [0,4]
a. Sketch the function on the given interval.
b. Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n= 4.
c. Use the sketch in part (a) to show which intervals of [0,4] make positive and negative contributions to the net area.
a. Choose the correct answer below.
OA.
OB.
D.
Ay
18+
Ay
18+
Ay
18-
Ay
48-
12-
12-
12-
12-
6-
6-
6-
0-
0-
0-
-6-
-6-
-6
-12-
12-
48-
-12-
-18-
-12-
-18
-
-18-
b. The net area, approximated using the left Riemann sum, is
The net area, approximated using the right Riemann sum, is
The net area, approximated using the midpoint Riemann sum, is
c. Which intervals of [0,4] make positive and negative contributions to the net area? Choose the correct answer below.
O A. Positive contributions on [2,4]; negative contributions on [0,2]
O B. Positive contributions on [0,3]; negative contributions on [3,4]
O C. Positive contributions on [3,4]; negative contributions on [0,3]
O D. Positive contributions on (0,2]; negative contributions on [2,4]
000
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Transcribed Image Text:*3. The following function is positive and negative on the given interval.
f(x) = 9 – x²; [0,4]
a. Sketch the function on the given interval.
b. Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n= 4.
c. Use the sketch in part (a) to show which intervals of [0,4] make positive and negative contributions to the net area.
a. Choose the correct answer below.
OA.
OB.
D.
Ay
18+
Ay
18+
Ay
18-
Ay
48-
12-
12-
12-
12-
6-
6-
6-
0-
0-
0-
-6-
-6-
-6
-12-
12-
48-
-12-
-18-
-12-
-18
-
-18-
b. The net area, approximated using the left Riemann sum, is
The net area, approximated using the right Riemann sum, is
The net area, approximated using the midpoint Riemann sum, is
c. Which intervals of [0,4] make positive and negative contributions to the net area? Choose the correct answer below.
O A. Positive contributions on [2,4]; negative contributions on [0,2]
O B. Positive contributions on [0,3]; negative contributions on [3,4]
O C. Positive contributions on [3,4]; negative contributions on [0,3]
O D. Positive contributions on (0,2]; negative contributions on [2,4]
000
DII
DD
esc
F4
F3
E5
F6
F7
F9
F10
F12
F1
F2
@
#
$
&
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4
5
6
7
8
delete
Q
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tab
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A
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