1 / 13

Riemann Sum Homework Review

Riemann Sum Homework Review. Pg. 505 # 7-10. n = 8. 1.00 1.02 1.06 1.12 1.19 1.27 1.34 1.42 1.50. X 0 = 0 X 1 = X 2 = X 3 = X 4 = X 5 = X 6 = X 7 = X 8 = 2. Y 0 = Y 1 = Y 2 = Y 3 = Y 4 = Y 5 = Y 6 = Y 7 = Y 8 =. 0.25 0.5 0.75 1 1.25 1.5 1.75.

hoyt-ramirez
Download Presentation

Riemann Sum Homework Review

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Riemann Sum Homework Review Pg. 505 # 7-10

  2. n = 8 1.00 1.02 1.06 1.12 1.19 1.27 1.34 1.42 1.50 X0 = 0 X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = 2 Y0 = Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = 0.25 0.5 0.75 1 1.25 1.5 1.75 LHS = 0.25 * 9.41 = 2.35 RHS = 0.25 * 9.90 = 2.48

  3. n = 8 1.00 1.02 1.06 1.12 1.19 1.27 1.34 1.42 1.50 X0 = 0 X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = 2 Y0 = Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = * 0.5 = 0.50 * 1 = 1.02 * 1 = 1.06 * 1 = 1.12 * 1 = 1.19 * 1 = 1.27 * 1 = 1.34 * 1 = 1.42 * 0.5 = 0.75 0.25 0.5 0.75 1 1.25 1.5 1.75 9.66 * 0.25 = 2.41 Trap.

  4. n = 8 X0 = 0 X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = 2 Y0.5 = 1.00 Y1.5 = 1.03 Y2.5 = 1.09 Y3.5 = 1.15 Y4.5 = 1.23 Y5.5 = 1.30 Y6.5 = 1.38 Y7.5 = 1.46 X0.5 = 0.125 X1.5 = 0.375 X2.5 = 0.625 X3.5 = 0.875 X4.5 = 1.135 X5.5 = 1.375 X6.5 = 1.625 X7.5 = 1.875 0.25 0.5 0.75 1 1.25 1.5 1.75 9.65 * 0.25 = 2.41 Midpt.

  5. n = 4 0.00 0.02 0.06 0.14 0.25 X0 = 0 X1 = X2 = X3 = X4 = 0.5 Y0 = Y1 = Y2 = Y3 = Y4 = 0.125 0.25 0.375 LHS = 0.218 * 0.125 = 0.027 RHS = 0.466 * 0.125 = 0.058

  6. n = 4 0.00 0.02 0.06 0.14 0.25 X0 = 0 X1 = X2 = X3 = X4 = 0.5 Y0 = Y1 = Y2 = Y3 = Y4 = * 0.5 = 0.00 * 1 = 0.02 * 1 = 0.06 * 1 = 0.14 * 0.5 = 0.12 0.125 0.25 0.375 0.342 * 0.125 = 0.043 Trap.

  7. n = 4 X0 = 0 X1 = X2 = X3 = X4 = 0.5 Y0.5 = 0.00 Y1.5 = 0.04 Y2.5 = 0.10 Y3.5 = 0.19 X0.5 = 0.0625 X1.5 = 0.1875 X2.5 = 0.3125 X3.5 = 0.4375 0.125 0.25 0.375 0.327 * 0.125 = 0.041 Midpt.

  8. n = 10 0.00 0.05 0.08 0.11 0.14 0.16 0.18 0.20 0.21 0.22 0.23 X0 = 1 X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = X9 = X10 = 2 Y0 = Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y10 = 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 LHS = 1.35 * 0.1 = 0.135 RHS = 1.58 * 0.1 = 0.158

  9. n = 10 0.00 0.05 0.08 0.11 0.14 0.16 0.18 0.20 0.21 0.22 0.23 X0 = 1 X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = X9 = X10 = 2 Y0 = Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = Y7 = Y8 = Y9 = Y10 = * 0.5 = 0.00 * 1 = 0.05 * 1 = 0.08 * 1 = 0.11 * 1 = 0.14 * 1 = 0.16 * 1 = 0.17 * 1 = 0.20 * 1 = 0.21 * 1 = 0.22 * 0.5 = 0.12 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Trapezoidal Rule 1.47 * 0.1 = 0.147

  10. n = 10 X0 = 1 X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = X8 = X8 = 2 Y0.5 = 0.02 Y1.5 = 0.07 Y2.5 = 0.10 Y3.5 = 0.13 Y4.5 = 0.15 Y5.5 = 0.17 Y6.5 = 0.19 Y7.5 = 0.20 X8.5 = 0.22 X9.5 = 0.23 X0.5 = 1.05 X1.5 = 1.15 X2.5 = 1.25 X3.5 = 1.35 X4.5 = 1.45 X5.5 = 1.55 X6.5 = 1.65 X7.5 = 1.75 X8.5 = 1.85 X9.5 = 1.95 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Midpoint Rule 1.47 * 0.1 = 0.147

  11. n = 6 1.00 0.76 0.33 0.12 0.05 0.02 0.01 X0 = 0 X1 = X2 = X3 = X4 = X5 = X6 = 3 Y0 = Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = 0.5 1 1.5 2 2.5 LHS = 2.28 * 0.5 = 1.14 RHS = 1.30 * 0.5 = 0.65

  12. n = 6 1.00 0.76 0.33 0.12 0.05 0.02 0.01 X0 = 0 X1 = X2 = X3 = X4 = X5 = X6 = 3 Y0 = Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = * 0.5 = 0.50 * 1 = 0.76 * 1 = 0.33 * 1 = 0.12 * 1 = 0.05 * 1 = 0.02 * 0.5 = 0.005 0.5 1 1.5 2 2.5 1.79 * 0.5 = 0.90 Trap.

  13. n = 6 X0 = 0 X1 = X2 = X3 = X4 = X5 = X6 = 3 Y0.5 = 0.94 Y1.5 = 0.53 Y2.5 = 0.20 Y3.5 = 0.07 Y4.5 = 0.03 Y5.5 = 0.02 X0.5 = 0.25 X1.5 = 0.75 X2.5 = 1.25 X3.5 = 1.75 X4.5 = 2.25 X5.5 = 2.75 0.5 1 1.5 2 2.5 1.79 * 0.5 = 0.90 Midpt.

More Related