Unformatted Attachment Preview
WebAssign is not supported for this device. Some features or content might not work. System
requirements
WebAssign
Welcome, eyadfarraj97@gmail.com@albany (sign out)
Tuesday, January 16 2018 05:59 PM EST
Home
My Assignments
Grades
MTH 241, section 241, Fall 2018
Communication
Calendar
My eBooks
Notifications
Help
My Options
Eyad Farraj
My Assignments
MTH 241, section 241, Fall 2018
Instructor: Corey Placito
Homework 15.1 (Homework)
Current Score : – / 38
Due : Friday, January 26 2018 11:59 PM EST
Print Assignment
Question
1
Points
2
3
4
5
6
7
8
9
Total
–/13 –/2 –/16 –/1 –/1 –/1 –/2 –/1 –/1
–/38 (0.0%)
Assignment Submission
For this assignment, you submit answers by question parts. The number of submissions remaining
for each question part only changes if you submit or change the answer.
Assignment Scoring
Your last submission is used for your score.
1.
–/13 points SCalc8 15.1.001.MI.SA.
My Notes
This question has several parts that must be completed sequentially. If you
skip a part of the question, you will not receive any points for the skipped
part, and you will not be able to come back to the skipped part.
Estimate the volume of the solid that lies below the surface z = xy and
above the following rectangle.
R=
(x, y) | 5 ≤ x ≤ 11, 3 ≤ y ≤ 7
Exercise (a)
Use a Riemann sum with m = 3, n = 2, and take the sample
point to be the upper right corner of each square.
Step 1
We are requested to use m = 3 and n = 2 over the rectangle
R = (x, y) | 5 ≤ x ≤ 11, 3 ≤ y ≤ 7
The subrectangles are, therefore, as
follows.
We can estimate the volume of the given solid using the
Riemann sum
3
2
f(xi, yj)ΔA,
with
f(x, y) = xy.
i = 1j = 1
Since 5 ≤ x ≤ 11 and m = 3, then Δx =
3 ≤ y ≤ 7 and n = 2, then Δy =
ΔA =
Submit
, and since
. Consequently, we have
.
Skip (you cannot come back)
Exercise (b)
Use the Midpoint Rule to estimate the volume of the solid.
Step 1
Recall that in part (a), we saw that the subrectangles are as
follows, with ΔA = 4.
Using the Midpoint Rule, the sample points are in the center of
each square. For example, when i = 1 and j = 1, we are
referring to the square in the lower left corner of the grid, with
center at (x, y) =
.
Submit
Submit Answer
2.
Skip (you cannot come back)
Save Progress
Practice Another Version
–/2 points SCalc8 15.1.001.MI.
My Notes
Estimate the volume of the solid that lies below the surface z = xy and
above the following rectangle.
R=
(x, y) | 4 ≤ x ≤ 10, 4 ≤ y ≤ 8
(a) Use a Riemann sum with m = 3, n = 2, and take the sample point to
be the upper right corner of each square.
(b) Use the Midpoint Rule to estimate the volume of the solid.
3.
–/16 points SCalc8 15.1.501.XP.MI.SA.
My Notes
This question has several parts that must be completed sequentially. If you
skip a part of the question, you will not receive any points for the skipped
part, and you will not be able to come back to the skipped part.
Tutorial Exercise
The figure shows level curves of a function f in the square R =
[0, 4] ⨯ [0, 4]. Use the Midpoint Rule with m = n = 2 to estimate
the following.
f(x, y) dA
R
How could you improve your estimate?
Step 1
We are asked to use m = n = 2, and, therefore, need to divide R
into 4 equal subrectangles, as follows.
Note that the subrectangles are actually squares. The area of
each square is
. Therefore, we have ΔA =
.
Submit
4.
Skip (you cannot come back)
–/1 points SCalc8 15.1.502.XP.
My Notes
Evaluate the double integral by first identifying it as the volume of a solid.
R
5.
2 dA, R = {(x, y) | −1 ≤ x ≤ 1, 1 ≤ y ≤ 6}
–/1 points SCalc8 15.1.503.XP.
My Notes
Evaluate the double integral by first identifying it as the volume of a solid.
R
6.
(4 − x) dA, R = {(x, y) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 4}
–/1 points SCalc8 15.1.506.XP.
My Notes
If R = [−3, 1] × [0, 2], use a Riemann sum with m = 4, n = 2 to estimate the
value of
(y2 − 2x2) dA. Take the sample points to be the upper left corners of
R
the squares.
7.
–/2 points SCalc8 15.1.508.XP.
My Notes
(a) Estimate the volume of the solid that lies below the surface z = 3x + 2y2 and
above the rectangle R = [0, 2] × [0, 4]. Use a Riemann sum with m = n = 2
and choose the sample points to be lower right corners.
(b) Use the Midpoint Rule to estimate the volume in part (a).
8.
–/1 points SCalc8 15.1.006.
My Notes
A 20-ft-by-30-ft swimming pool is filled with water. The depth is measured at
5-ft intervals, starting at one corner of the pool, and the values are recorded
in the table. Estimate the volume of water using the Midpoint Rule with m =
2 and n = 3.
ft3
9.
x\y
0
5
10
15
20
25
30
0
2
4
5
6
7
8
8
5
2
4
5
5
8
10
8
10
2
4
6
8
10
12
10
15
2
3
4
5
6
7
7
20
2
2
2
2
3
4
4
–/1 points SCalc8 15.1.005.
My Notes
Let V be the volume of the solid that lies under the graph of f(x,y) and above
the rectangle given by 3 ≤ x ≤ 5, 1 ≤ y ≤ 5. We use the lines x = 4 and
y = 3 to divide R into subrectangles. Let L and U be the Riemann sums
computed using lower left corners and upper right corners, respectively.
Without calculating the numbers V, L, and U, arrange them in increasing
order.
f(x, y) =
50 − x2 − y2
U