The Figure Shows Level Curves Of A Function In The Square R 0 4 X 0 4 Use The Midpoint Rule With M N 2 To E 1 (39.48 KiB) Viewed 23 times
The figure shows level curves of a function in the square R = [0, 4] x [0, 4). Use the Midpoint Rule with m = n = 2 to estimate the following. x STA FOX ) DA How could you improve your estimate? y 13 14 15 16 12 2 11 10 2 Step 1 We are asked to use m= n = 2, and, therefore, need to divide R into 4 equal subrectangles, as follows. y 13 14 15 116 12 2 11 10 2 Note that the subrectangles are actually squares. The area of each square is Therefore, we have A4 - 4 4
Step 2 When i = 1 and j = 1, we are referring to the coordinates of the rectangle in the lower left corner of the grid. We are told to use the midpoint as a sample point. For i = 1 and j = 1, the sample point would, therefore, be (x,y) = ( 1,1 1.1 Step 3 ,1), when i = 1 and j = 2, the sample point is (x, y) = (1, 3 ), and when i = 2 and j = 2, the Similarly, when i = 2 and j = 1, the sample point is (x, y) = ( 3 sample point is (x, y) = ( 3 , 3). Step 4 We must estimate the value of f(x,y) at each of the sample points. Based on the contours, when i = 1 and j = 1, a good choice for an estimate of f(1,1) is x Submit Skip (you cannot come back) Need Help? Read It
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