Варианты и ответы

Обозначения:

ErrHauss3, ErrHauss4 – погрешность вычислений по формуле Гаусса с тремя и четырьмя узлами.

ErrNewtCot3, ErrNewtCot4 – погрешность вычислений по формуле Ньютона-Котеса с тремя и четырьмя узлами.

ErrSimps – погрешность вычислений по формуле Симпсона при разбиении отрезка интегрирования [a,b] на 4m подотрезков.

ErrAtk – погрешность вычислений по формуле Эйткена при использовании разбиений отрезка интегрирования [a,b] на m, 2 m и 4m подотрезков.

1. а) б)

ErrHauss3=-0.000330 ErrHauss4=-0.0000125 ErrSimps=-0.000894 m=2

ErrNewtCot3=0.0220 ErrHauss4=0.00589 ErrAtk=0.0000158 p=1.48

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2. а) б)

ErrHauss3=0.0982 ErrHauss4=0. ErrSimps=-0.00130 m=2

ErrNewtCot3=-0.196 ErrNewtCot4=-0.177 ErrAtk=-0.0000752 p=1.60

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3. а) б)

ErrHauss3=-0.0000646 ErrHauss4=-0.00000191 ErrSimps=-0.00298 m=2

ErrNewtCot3=0.00698 ErrNewtCot4=0.00158 ErrAtk=0.0000944 p=1.25

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4. а) б)

ErrHauss3=0. ErrHauss4=0. ErrSimps=-0.00255 m=2

ErrNewtCot3=-0.393 ErrNewtCot4=-0.218 ErrAtk=0.0000243 p=1.52

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5. а) б)

ErrHauss3=-3.3*10^-10 ErrHauss4=-3.6*10^-15 ErrSimps=-0.00359 m=2

ErrNewtCot3=0.000377 ErrNewtCot4=7.3*10^-6 ErrAtk=4.3*10^-6 p=1.50

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6. а) б)

ErrHauss3=-0.000132 ErrHauss4=0.0000410 ErrSimps=-0.0171 m=2

ErrNewtCot3=-0.00144 ErrNewtCot4=0.00602 ErrAtk=0.0000603 p=1.33

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7. а) б)

ErrHauss3=-0.00676 ErrHauss4=-0.00388 ErrSimps=-0.00127 m=2

ErrNewtCot3=0.0301 ErrNewtCot4=0.0238 ErrAtk=0.0000212 p=1.48

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8. а) б)

ErrHauss3=-0.00369 ErrHauss4=-0.00148 ErrSimps=-0.0209 m=2

ErrNewtCot3=0.0401 ErrNewtCot4=0.0252 ErrAtk=-0.00194 p=1.64

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9. а) б)

ErrHauss3=-9.6*10^-7 ErrHauss4=-1.1*10^-10 ErrSimps=-0.000630 m=2

ErrNewtCot3=-0.0232 ErrNewtCot4=0.00173 ErrAtk=0.0000398 p=1.43

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10. а) б)

ErrHauss3=0.0569 ErrHauss4=0.0333 ErrSimps=-0.00735 m=2

ErrNewtCot3=-0.324 ErrNewtCot4=-0.201 ErrAtk=-0.000308 p=1.58

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11. а) б)

ErrHauss3=0.0163 ErrHauss4=0.00913 ErrSimps=-0.00342 m=2

ErrNewtCot3=-0.0735 ErrNewtCot4=-0.0574 ErrAtk=-0.0000614 p=1.36

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12. а) б)

ErrHauss3=-0.00200 ErrHauss4=-0.000676 ErrSimps=-0.00255 m=2

ErrNewtCot3=0.0214 ErrNewtCot4=0.0126 ErrAtk=-0.0000273 p=1.52

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13. а) б)

ErrHauss3=0.00876 ErrHauss4=0.00492 ErrSimps=-0.00190 m=2

ErrNewtCot3=-0.0394 ErrNewtCot4=-0.0309 ErrAtk=-0.0000260 p=1.49

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14. а) б)

ErrHauss3=0.000240 ErrHauss4=-6.1*10^-6 ErrSimps=-0.00717 m=2

ErrNewtCot3=0.0106 ErrNewtCot4=0.00552 ErrAtk=0.0000411 p=1.49

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15. а) б)

ErrHauss3=0.0268 ErrHauss4=0.00118 ErrSimps=-0.00431 m=2

ErrNewtCot3=-0.0524 ErrNewtCot4=-0.0555 ErrAtk=-0.0000770 p=1.36

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16. а) б)

ErrHauss3=-0.00222 ErrHauss4=-0.00113 ErrSimps=-0.00725 m=2

ErrNewtCot3=0.0484 ErrNewtCot4=0.0337 ErrAtk=-0.000158 p=1.54

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17. а) б)

ErrHauss3=0. ErrHauss4=0. ErrSimps=-0.00386 m=2

ErrNewtCot3=-0.393 ErrNewtCot4=-0.218 ErrAtk=-0.000160 p=1.56

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18. а) б)

ErrHauss3=-7.5*10^-6 ErrHauss4=-1.7*10^-7 ErrSimps=-0.00118 m=2

ErrNewtCot3=-0.000354 ErrNewtCot4=0.000252 ErrAtk=-0.000118 p=1.65

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19. а) б)

ErrHauss3=-0.0982 ErrHauss4=0. ErrSimps=-0.0145 m=2

ErrNewtCot3=0.589 ErrNewtCot4=0.395 ErrAtk=-0.000181 p=1.53

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20. а) б)

ErrHauss3=-0.0000237 ErrHauss4=5.9*10^-6 ErrSimps=-0.00127 m=2

ErrNewtCot3=0.00361 ErrNewtCot4=0.00510 ErrAtk=1.5*10^-6 p=1.53

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21. а) б)

ErrHauss3=-0.0000171 ErrHauss4=-4.4*10^-7 ErrSimps=-0.00124 m=2

ErrNewtCot3=0.00246 ErrNewtCot4=0.000505 ErrAtk=0.0000511 p=1.44

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22. а) б)

ErrHauss3=-0.0000328 ErrHauss4=-1.2*10^-6 ErrSimps=-0.00717 m=2

ErrNewtCot3=0.00191 ErrNewtCot4=0.00185 ErrAtk=0.0000411 p=1.49

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23. а) б)

ErrHauss3=0.00142 ErrHauss4=0.000188 ErrSimps=-0.00560 m=2

ErrNewtCot3=-0.0169 ErrNewtCot4=-0.00902 ErrAtk=0.000192 p=1.45

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24. а) б)

ErrHauss3=0.00349 ErrHauss4=0.00126 ErrSimps=-0.0212 m=2

ErrNewtCot3=-0.0348 ErrNewtCot4=-0.0210 ErrAtk=-0.00326 p=1.74

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25. а) б)

ErrHauss3=-0.0134 ErrHauss4=-0.00748 ErrSimps=-0.00128 m=2

ErrNewtCot3=0.0605 ErrNewtCot4=0.0472 ErrAtk=-0.0000279 p=1.54

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26. а) б)

ErrHauss3=-0.00150 ErrHauss4=-0.000569 ErrSimps=-0.00181 m=2

ErrNewtCot3=0.0133 ErrNewtCot4=0.00837 ErrAtk=0.000255 p=1.54

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27. а) б)

ErrHauss3=-0.00303 ErrHauss4=-0.00122 ErrSimps=-0.00322 m=2

ErrNewtCot3=0.0336 ErrNewtCot4=0.0209 ErrAtk=-0.000152 p=1.57

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28. а) б)

ErrHauss3=-0.0000119 ErrHauss4=-2.5*10^-7 ErrSimps=-0.00255 m=2

ErrNewtCot3=-0.00112 ErrNewtCot4=0.000501 ErrAtk=-0.0000273 p=1.52

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29. а) б)

ErrHauss3=-0.000162 ErrHauss4=-0.0000381 ErrSimps=-0.00894 m=2

ErrNewtCot3=-0.00241 ErrNewtCot4=0.00164 ErrAtk=-0.000753 p=1.64

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30. а) б)

ErrHauss3=0.0000208 ErrHauss4=5.6*10^-7 ErrSimps=-0.000669 m=2

ErrNewtCot3=0.00182 ErrNewtCot4=0.000786 ErrAtk=-0.0000988 p=1.74

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31. а) б)

ErrHauss3=0.000142 ErrHauss4=-4.9*10^-6 ErrSimps=-0.000630 m=2

ErrNewtCot3=0.00332 ErrNewtCot4=0.00133 ErrAtk=0.0000398 p=1.43

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32. а) б)

ErrHauss3=0.000325 ErrHauss4=0.0000266 ErrSimps=-0.00339 m=2

ErrNewtCot3=-0.00597 ErrNewtCot4=-0.00302 ErrAtk=2.3*10^-6 p=1.33

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33. а) б)

ErrHauss3=0.000326 ErrHauss4=-0.0000128 ErrSimps=-0.0147 m=2

ErrNewtCot3=0.0399 ErrNewtCot4=0.0170 ErrAtk=-0.000783 p=1.58

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34. а) б)

ErrHauss3=-0.00218 ErrHauss4=-0.000632 ErrSimps=-0.0145 m=2

ErrNewtCot3=-0.0482 ErrNewtCot4=-0.0235 ErrAtk=-0.000229 p=1.53

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35. а) б)

ErrHauss3=0.00164 ErrHauss4=-0.0000587 ErrSimps=-0.0725 m=2

ErrNewtCot3=0.00164 ErrNewtCot4=-0.00410 ErrAtk=-0.000158 p=1.54

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36. а) б)

ErrHauss3=0. ErrHauss4=0. ErrSimps=-0.00190 m=2

ErrNewtCot3=0. ErrNewtCot4=0. ErrAtk=0.0000260 p=1.49

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37. а) б)

ErrHauss3=-0.00234 ErrHauss4=-0.00114 ErrSimps=-0.0102 m=2

ErrNewtCot3=0.0476 ErrNewtCot4=-0.0334 ErrAtk=-0.0000970 p=1.52

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38. а) б)

ErrHauss3=-0.00211 ErrHauss4=-0.00113 ErrSimps=-0.0173 m=2

ErrNewtCot3=0.0492 ErrNewtCot4=-0.0339 ErrAtk=-0.000309 p=1.37

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39. а) б)

ErrHauss3=0.00141 ErrHauss4=0.00194 ErrSimps=-0.00366 m=2

ErrNewtCot3=0.00489 ErrNewtCot4=0.000219 ErrAtk=-0.000258 p=1.60

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40. а) б)

ErrHauss3=-0.000117 ErrHauss4=-1.8*10^-6 ErrSimps=-0.00128 m=2

ErrNewtCot3=-0.000777 ErrNewtCot4=-0.000222 ErrAtk=-0.0000405 p=1.55

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41. а) б)

ErrHauss3=-0.000301 ErrHauss4=-0.0000894 ErrSimps=-0.00126 m=2

ErrNewtCot3=-0.0162 ErrNewtCot4=0.0103 ErrAtk=0.0000170 p=1.48

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42. а) б)

ErrHauss3=0.00381 ErrHauss4=0.00214 ErrSimps=-0.000890 m=2

ErrNewtCot3=-0.0171 ErrNewtCot4=-0.0134 ErrAtk=0.0000123 p=1.48

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43. а) б)

ErrHauss3=-0.00116 ErrHauss4=-0.000655 ErrSimps=-0.00180 m=2

ErrNewtCot3=0.0254 ErrNewtCot4=0.0135 ErrAtk=0.0000101 p=1.51

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44. а) б)

ErrHauss3=-0.00150 ErrHauss4=-0.000572 ErrSimps=-0.00192 m=2

ErrNewtCot3=0.0142 ErrNewtCot4=0.00878 ErrAtk=-0.0000587 p=1.55

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45. а) б)

ErrHauss3=-0.00214 ErrHauss4=-0.000642 ErrSimps=-0.00720 m=2

ErrNewtCot3=0.0166 ErrNewtCot4=0.0106 ErrAtk=-0.000298 p=1.55

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46. а) б)

ErrHauss3=0.000132 ErrHauss4=-0.0000410 ErrSimps=-0.00362 m=2

ErrNewtCot3=0.00144 ErrNewtCot4=-0.00602 ErrAtk=-0.0000615 p=1.53

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47. а) б)

ErrHauss3=-0.0982 ErrHauss4=0. ErrSimps=-0.00339 m=2

ErrNewtCot3=0.196 ErrNewtCot4=0.177 ErrAtk=2.3*10^-6 p=1.33

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48. а) б)

ErrHauss3=0.0220 ErrHauss4=0.0122 ErrSimps=-0.0110 m=2

ErrNewtCot3=-0.109 ErrNewtCot4=-0.0769 ErrAtk=-0.000445 p=1.58

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49. а) б)

ErrHauss3=-0.00003423 ErrHauss4=-0.0000317 ErrSimps=-0.0147 m=2

ErrNewtCot3=-0.00413 ErrNewtCot4=-0.0114 ErrAtk=-0.000798 p=1.59

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50. а) б)

ErrHauss3=-0.00153 ErrHauss4=0. ErrSimps=-0.00364 m=2

ErrNewtCot3=-0.00920 ErrNewtCot4=-0.00617 ErrAtk=-0.000152 p=1.56

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