- Your Task Is To Find The Sum Of The Areas Of The Respons Bounded By The Taxis And The Graph Of The Following Function F 1 (20.76 KiB) Viewed 23 times
- Your Task Is To Find The Sum Of The Areas Of The Respons Bounded By The Taxis And The Graph Of The Following Function F 2 (26.81 KiB) Viewed 23 times
- Your Task Is To Find The Sum Of The Areas Of The Respons Bounded By The Taxis And The Graph Of The Following Function F 3 (55.78 KiB) Viewed 23 times
- Your Task Is To Find The Sum Of The Areas Of The Respons Bounded By The Taxis And The Graph Of The Following Function F 4 (52.26 KiB) Viewed 23 times
You should 1. Use Excel to plot the graph of f(x). This will help you to locate the roots of the function. You may need to experiment a little with the range over which you plot your graph sure that you have located all the regions of interest. 2. Use Newton's method to approximate the roots of the function. You should use a tolerance of = 10- 3. Use the midpoint rule to approximate the areas of each of the regions bounded by the raxis the graph of J(1). You shondusen - 100 rectangles 4. If there is more than one such region, sum the arms of these regions to get your final answer. 5. Your final awer should be correct to at least 5 decimal places. You must submit a macrocabled Excel workbook containing your graph and the code you used to find your answer. The final answer should be clearly displayed on the spreadsheet.
Your tuk stof the theme of the bottled the map of the lower (*) ?-712+102-1 Note that the derivative) x- 1112 1 Newton-Raphson's Method f(x) f'(x) X 3 0 0.9 -0.342 3.85 0.9888311690 4 1 0.988831 -0.03402 3.091959 0.99983368733 5 2 0.999834 -0.0005 3.001364 0.99999996221 6 3 1 -1.1E-07 3 1.00000000000 74 1 0 3 1.00000000000 2 k NR method for the first *4 = 1 A B c D F G H y=f(x) -1 -30.4 15 -0.5 -17.1 10 0 -8.1 5 0.5 -2.65 (1.0) 1 0 0 1.5 0.6 O -5 2 -0.1 (1.953.0) (4.147.0) -10 2.5 -1.35 3 -15 -2.4 3.5 -2.5 -20 4 -0.9 -25 4.5 3.15 -30 5 10.4 -35 2. Newton's wwthod to me that the Yankee C Newton-Raphson's Method 1 Newton-Raphson's Method X (x) 2 * * f(x) 1'(x) X 0 4 -0.9 5.4 4.166666667 30 1.9 0.108 -1.95 1.95538461 1 4.166667 0.140741 7.116667 4.14689045013 4 1 1.955385 -0.00412 -2.09587 1.95341667€ 2 4.14689 0.002104 6.904257 4.1465856818 5 2 1.953417 -4.8E-06 -2.09101 1.95341439C 3 4.146586 4.96E-07 6.901002 4.14658560997 6 3 1.953414 -6.5E-12 -2.091 1.953414390 4 4.146586 2.31E-14 6.901001 4.14658560991 7 4 1.953414 0 -2.091 1.95341439C 5 4.146586 0 6.901001 4.14658560997 The second zoro X X1.95341439 3 4.14658561 fix] The third roof foxzo is. C'To lestred accuracy)
3. Use the midpoint rule to approximate the areas of each of the region the map of ). You should - 100 rectangles midpoint method $1.95341(-8.1 + 14.2 x - 7.1 x² + xº)dx z 0.00953414 292 (0.0142082 +0.0282304 n - 0.00037139 na +8.66653 x 10-?n?) 41.95341 f(x) dx=h (1+h(+ n)) where f(x) = x3 – 7.1 x2 + 14.2 x - 8.1 h = (1.95341 - 1)/100 = 0.00953414 A=0.3856621833349602 midpoint method S4959659 (-8.1 + 14.2 x - 7.1 x2 + x°) d x 11.95341 0.0219317 2.2% (-0.0230774 -0.0464476n -0.000580499 na +0.0000105492 n) 51995341° f(x) dx = h 2220 |(1.95341 + h (4 + n)) 4.14659 } where f(x) = x3 - 7.1 x2 + 14.2 x - 8.1 h =(4.14659 - 1.95341)/100 = 0.0219317 B = -3.604474350419935 4. If there is more than one machen, um term of the regions to pet your finner The total area with sen A+B = -3.2188121670849748 Total area with absolute vores = (Al + 161 valves 3.9901365337548952 5. Your final should be correct to at least 5 decimal places = 3.99014