Business Calc Homework w answers_Part_56

Business Calc Homework w answers_Part_56 - 276 Section 6.6...

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13. To find the approximate values, set y 1 5 x 2 y and use EULERT and IMPEULT with initial values x 5 0 and y 5 1 and step size 0.1 for 20 points. The exact values are given by y 5 x 2 1 1 2 e 2 x . 276 Section 6.6 x y (Euler) y 12 improved Euler y (exact) 0 1 1 1 0.1 0.9000 0.9100 0.9097 0.2 0.8200 0.8381 0.8375 0.3 0.7580 0.7824 0.7816 0.4 0.7122 0.7416 0.7406 0.5 0.6810 0.7142 0.7131 0.6 0.6629 0.6988 0.6976 0.7 0.6566 0.6944 0.6932 0.8 0.6609 0.7000 0.6987 0.9 0.6748 0.7145 0.7131 1.0 0.6974 0.7371 0.7358 1.1 0.7276 0.7671 0.7657 1.2 0.7649 0.8037 0.8024 1.3 0.8084 0.8463 0.8451 1.4 0.8575 0.8944 0.8932 1.5 0.9118 0.9475 0.9463 1.6 0.9706 1.0050 1.0038 1.7 1.0335 1.0665 1.0654 1.8 1.1002 1.1317 1.1306 1.9 1.1702 1.2002 1.1991 2.0 1.2432 1.2716 1.2707 Error (Euler) Error improved Euler 0 0 0.0097 0.0003 0.0175 0.0006 0.0236 0.0008 0.0284 0.0010 0.0321 0.0011 0.0347 0.0012 0.0366 0.0012 0.0377 0.0013 0.0383 0.0013 0.0384 0.0013 0.0381 0.0013 0.0375 0.0013 0.0367 0.0013 0.0357 0.0012 0.0345 0.0012 0.0332 0.0012 0.0318 0.0011 0.0304 0.0011 0.0290 0.0010 0.0275 0.0010
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14. To find the approximate values, set y 1 5 y 2 e 2 x 1 1 and use EULERT and IMPEULT with initial values x 5 0 and y 52 1 and step size 0.1 for 20 points. The exact values are given by y 5 e x 2 e 2 x 2 1. 15. (a) } d d y x } 5 2 y 2 ( x 2 1) } d y y 2 } 5 2( x 2 1) dx E y 2 2 dy 5 E (2 x 2 2) dx 2 y 2 1 5 x 2 2 2 x 1 C Initial value: y (2) 52} 1 2 } 2 5 2 2 2 2(2) 1 C 2 5 C Solution: 2 y 2 1 5 x 2 2 2 x 1 2 or y } x 2 2 2 1 x 1 2 } y (3) } 3 2 2 2 1 (3) 1 2 }52} 1 5 }52 0.2 (b) To find the approximation, set y 1 5 2 y 2 ( x 2 1) and use EULERT with initial values x 5 2 and y 1 2 } and step size 0.2 for 5 points. This gives y (3) < 2 0.1851; error < 0.0149. (c) Use step size 0.1 for 10 points. This gives y (3) < 2 0.1929; error < 0.0071. (d) Use step size 0.05 for 20 points. This gives y (3) < 2 0.1965; error < 0.0035. Section 6.6 277 x y (Euler) y 12 improved Euler y (exact) 0 2 1 2 1 2 1 0.1 2 1.1000 2 1.1161 2 1.1162 0.2 2 1.2321 2 1.2700 2 1.2704 0.3 2 1.4045 2 1.4715 2 1.4723 0.4 2 1.6272 2 1.7325 2 1.7337 0.5 2 1.9125 2 2.0678 2 2.0696 0.6 2 2.2756 2 2.4954 2 2.4980 0.7 2 2.7351 2 3.0378 2 3.0414 0.8 2 3.3142 2 3.7224 2 3.7275 0.9 2 4.0409 2 4.5832 2 4.5900 1.0 2 4.9499 2 5.6616 2 5.6708 1.1 2 6.0838 2 7.0087 2 7.0208 1.2 2 7.4947 2 8.6872 2 8.7031 1.3 2 9.2465 2 10.7738 2 10.7944 1.4 2 11.4175 2 13.3628 2 13.3894 1.5 2 14.1037 2 16.5696 2 16.6038 1.6 2 17.4227 2 20.5358 2 20.5795 1.7 2 21.5182 2 25.4345 2 25.4902 1.8 2 26.5664 2 31.4781 2 31.5486 1.9 2 32.7829 2 38.9262 2 39.0153 2.0 2 40.4313 2 48.0970 2 48.2091 Error (Euler) Error improved Euler 0 0 0.0162 0.0002 0.0383 0.0004 0.0677 0.0007 0.1065 0.0012 0.1571 0.0018 0.2224 0.0026 0.3063 0.0037 0.4133 0.0050 0.5492 0.0068 0.7209 0.0092 0.9370 0.0121 1.2084 0.0159 1.5480 0.0206 1.9719 0.0267 2.5001 0.0342 3.1568 0.0437 3.9720 0.0556 4.9822 0.0705 6.2324 0.0891 7.7778 0.1121
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16. (a) } d d
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This document was uploaded on 10/31/2011 for the course MAC 2311 at University of Florida.

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Business Calc Homework w answers_Part_56 - 276 Section 6.6...

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