Question

roo _72 05 Estimate the numerical value of fºe-x dx by writing it as the sum of ſex" dx and er dx, then: (a) Use Simpson's Rule with four subintervals (i.e. n = 4) to approximate ("e-*dx. Give three decimal places. An error calculation is not required. 4 pts (b) Show that (*e-x dx < 50e-5x dx. Calculate the value of bioe-5x dx and use this to show that the value of L ex dx is negligible.5 pts so del est u n like to como (c) Take your answer to part (a) as a good approximation of ſex dx. 1 pt (If you would like to calculate a maximum error in part (a) for your own interest this is a good exercise but is not part of the assignment.) cada per la part of or your own interest this generar

Answer 1

- 4 1-25 A @met, 11-*de lfcus diz haba 5 -1.25., Ko-o, Hi= 0+ih x=ih xo=0 | 2 = 1.25 | x2=2.5 X 2= 3.75 / X4-5) f(es) 0.20361 0.00173 | 72x10 + 1.30 1157 |

- In Secode="[ f(46)44 f(x) +2 f(*) + 4 f(x) + f(and] = 1-3 - [1 +4(0,2096) +2(0.00193)+4(10x15 73+1 39210"] ~1.25. *1.84230312 ~10.768 Deo et ésx for all 5<x4 Us

for an orsa 2.7776x1012 1-5 da <2.77768 10 12 < 0.768 Now. Perde - TIS - 274620 > (2'da < 2:77702415" <<< 0768 > *< S'Eco de ce: lodde fakte 20.262