Multivariable Homework

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Hello ALL, This is Multivariable Calculus Homework that needs to be completed ASAP. You must have a good background in this topic. I have a hard time with these and the deadline is coming up.

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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
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