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Rearrangement Method x=g(x) [Fixed Point Iteration]

Rearrangement Method x=g(x) [Fixed Point Iteration]
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2013-06-19 19:54
FunctionCalculusDerivativeOptimizationGraphing
In collections A Level: Numerical Methods for Solving Equations
This example demonstrates the numerical method for finding roots of f(x)=0 by rearranging it into x=g(x) and iterating x_{n+1}=g(x_n). ① It visually illustrates the fixed point iteration process, showing the convergence of the iteration sequence. ② Core mathematical concepts include fixed points, iteration sequences, convergence, and function graphs. ③ Construction highlights the use of GeoGebra commands like Point, Derivative, Text, Textfield, Segment, with key objects such as function f, its derivative f', iteration points posX, posY, zoom parameters zoomX, zoomY, etc. ④ Suitable for high school and above learners to understand the application of numerical methods in equation solving.

GeoGebra Commands & Parameters

  1. Point(xAxis) → x_0
  2. Derivative(f) → f'
  3. Text("x_0=", A) → F1
  4. Textfield(f) → inputBox1
  5. Text("x_" * B11 + "_" * A11 * "=", (x(A), y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → F11
  6. Text("x_" * B12 + "_" * A12 * "=", (x(A), y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → F12
  7. Text("x_" * B13 + "_" * A13 * "=", (x(A), y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → F13
  8. Text("x_" * B14 + "_" * A14 * "=", (x(A), y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → F14
  9. Text("x_" * B15 + "_" * A15 * "=", (x(A), y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → F15
  10. Text("x_" * B16 + "_" * A16 * "=", (x(A), y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → F16
  11. Text("x_" * B17 + "_" * A17 * "=", (x(A), y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → F17
  12. Text("x_" * B18 + "_" * A18 * "=", (x(A), y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → F18
  13. Text("x_" * B19 + "_" * A19 * "=", (x(A), y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → F19
  14. Text("x_" * B20 + "_" * A20 * "=", (x(A), y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → F20
  15. Text("x_" * B21 + "_" * A21 * "=", (x(A), y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → F21
  16. Text("x_" * B22 + "_" * A22 * "=", (x(A), y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → F22
  17. Text("x_" * B23 + "_" * A23 * "=", (x(A), y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → F23
  18. Text("x_" * B24 + "_" * A24 * "=", (x(A), y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → F24
  19. Text("x_" * B25 + "_" * A25 * "=", (x(A), y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → F25
  20. Text("x_" * B26 + "_" * A26 * "=", (x(A), y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → F26
  21. Text(C11, (x(A) + 0.4 * zoomX, y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → G11
  22. Text(C12, (x(A) + 0.4 * zoomX, y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → G12
  23. Text(C13, (x(A) + 0.4 * zoomX, y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → G13
  24. Text(C14, (x(A) + 0.4 * zoomX, y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → G14
  25. Text(C15, (x(A) + 0.4 * zoomX, y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → G15
  26. Text(C16, (x(A) + 0.4 * zoomX, y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → G16
  27. Text(C17, (x(A) + 0.4 * zoomX, y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → G17
  28. Text(C18, (x(A) + 0.4 * zoomX, y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → G18
  29. Text(C19, (x(A) + 0.4 * zoomX, y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → G19
  30. Text(C20, (x(A) + 0.4 * zoomX, y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → G20
  31. Text(C21, (x(A) + 0.4 * zoomX, y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → G21
  32. Text(C22, (x(A) + 0.4 * zoomX, y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → G22
  33. Text(C23, (x(A) + 0.4 * zoomX, y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → G23
  34. Text(C24, (x(A) + 0.4 * zoomX, y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → G24
  35. Text(C25, (x(A) + 0.4 * zoomX, y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → G25
  36. Text(C26, (x(A) + 0.4 * zoomX, y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → G26
  37. Text("x_" * A10 * "=", (x(A), y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → F10
  38. Text("x_" * A2 * "=", (x(A), y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → F2
  39. Text("x_" * A3 * "=", (x(A), y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → F3
  40. Text("x_" * A4 * "=", (x(A), y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → F4
  41. Text("x_" * A5 * "=", (x(A), y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → F5
  42. Text("x_" * A6 * "=", (x(A), y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → F6
  43. Text("x_" * A7 * "=", (x(A), y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → F7
  44. Text("x_" * A8 * "=", (x(A), y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → F8
  45. Text("x_" * A9 * "=", (x(A), y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → F9
  46. Text(C10, (x(A) + 0.4 * zoomX, y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → G10
  47. Text(C2, (x(A) + 0.4 * zoomX, y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → G2
  48. Text(C3, (x(A) + 0.4 * zoomX, y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → G3
  49. Text(C4, (x(A) + 0.4 * zoomX, y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → G4
  50. Text(C5, (x(A) + 0.4 * zoomX, y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → G5
  51. Text(C6, (x(A) + 0.4 * zoomX, y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → G6
  52. Text(C7, (x(A) + 0.4 * zoomX, y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → G7
  53. Text(C8, (x(A) + 0.4 * zoomX, y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → G8
  54. Text(C9, (x(A) + 0.4 * zoomX, y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → G9
  55. Text(C1, (x(A) + 0.4 * zoomX, y(A))) → G1
  56. Text(C27, (x(A) + 2.1 * zoomX, y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → G27
  57. Text("x_" * B27 + "_" * A27 * "=", (x(A) + 1.7 * zoomX, y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → F27
  58. Text("x_" * B28 + "_" * A28 * "=", (x(A) + 1.7 * zoomX, y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → F28
  59. Text("x_" * B29 + "_" * A29 * "=", (x(A) + 1.7 * zoomX, y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → F29
  60. Text("x_" * B30 + "_" * A30 * "=", (x(A) + 1.7 * zoomX, y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → F30
  61. Text("x_" * B31 + "_" * A31 * "=", (x(A) + 1.7 * zoomX, y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → F31
  62. Text("x_" * B32 + "_" * A32 * "=", (x(A) + 1.7 * zoomX, y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → F32
  63. Text("x_" * B33 + "_" * A33 * "=", (x(A) + 1.7 * zoomX, y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → F33
  64. Text("x_" * B34 + "_" * A34 * "=", (x(A) + 1.7 * zoomX, y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → F34
  65. Text("x_" * B35 + "_" * A35 * "=", (x(A) + 1.7 * zoomX, y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → F35
  66. Text("x_" * B36 + "_" * A36 * "=", (x(A) + 1.7 * zoomX, y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → F36
  67. Text("x_" * B37 + "_" * A37 * "=", (x(A) + 1.7 * zoomX, y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → F37
  68. Text("x_" * B38 + "_" * A38 * "=", (x(A) + 1.7 * zoomX, y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → F38
  69. Text("x_" * B39 + "_" * A39 * "=", (x(A) + 1.7 * zoomX, y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → F39
  70. Text("x_" * B40 + "_" * A40 * "=", (x(A) + 1.7 * zoomX, y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → F40
  71. Text("x_" * B41 + "_" * A41 * "=", (x(A) + 1.7 * zoomX, y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → F41
  72. Text("x_" * B42 + "_" * A42 * "=", (x(A) + 1.7 * zoomX, y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → F42
  73. Text("x_" * B43 + "_" * A43 * "=", (x(A) + 1.7 * zoomX, y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → F43
  74. Text("x_" * B44 + "_" * A44 * "=", (x(A) + 1.7 * zoomX, y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → F44
  75. Text("x_" * B45 + "_" * A45 * "=", (x(A) + 1.7 * zoomX, y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → F45
  76. Text("x_" * B46 + "_" * A46 * "=", (x(A) + 1.7 * zoomX, y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → F46
  77. Text("x_" * B47 + "_" * A47 * "=", (x(A) + 1.7 * zoomX, y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → F47
  78. Text("x_" * B48 + "_" * A48 * "=", (x(A) + 1.7 * zoomX, y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → F48
  79. Text("x_" * B49 + "_" * A49 * "=", (x(A) + 1.7 * zoomX, y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → F49
  80. Text("x_" * B50 + "_" * A50 * "=", (x(A) + 1.7 * zoomX, y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → F50
  81. Text("x_" * B51 + "_" * A51 * "=", (x(A) + 1.7 * zoomX, y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → F51
  82. Text("x_" * B52 + "_" * A52 * "=", (x(A) + 1.7 * zoomX, y(A) - (B27 * 10 + A27) * 0.15 * zoomY)) → F52
  83. Text("x_" * B53 + "_" * A53 * "=", (x(A) + 1.7 * zoomX, y(A) - (B28 * 10 + A28) * 0.15 * zoomY)) → F53
  84. Text("x_" * B54 + "_" * A54 * "=", (x(A) + 1.7 * zoomX, y(A) - (B29 * 10 + A29) * 0.15 * zoomY)) → F54
  85. Text("x_" * B55 + "_" * A55 * "=", (x(A) + 1.7 * zoomX, y(A) - (B30 * 10 + A30) * 0.15 * zoomY)) → F55
  86. Text("x_" * B56 + "_" * A56 * "=", (x(A) + 1.7 * zoomX, y(A) - (B31 * 10 + A31) * 0.15 * zoomY)) → F56
  87. Text("x_" * B57 + "_" * A57 * "=", (x(A) + 1.7 * zoomX, y(A) - (B32 * 10 + A32) * 0.15 * zoomY)) → F57
  88. Text("x_" * B58 + "_" * A58 * "=", (x(A) + 1.7 * zoomX, y(A) - (B33 * 10 + A33) * 0.15 * zoomY)) → F58
  89. Text("x_" * B59 + "_" * A59 * "=", (x(A) + 1.7 * zoomX, y(A) - (B34 * 10 + A34) * 0.15 * zoomY)) → F59
  90. Text("x_" * B60 + "_" * A60 * "=", (x(A) + 1.7 * zoomX, y(A) - (B35 * 10 + A35) * 0.15 * zoomY)) → F60
  91. Text("x_" * B61 + "_" * A61 * "=", (x(A) + 1.7 * zoomX, y(A) - (B36 * 10 + A36) * 0.15 * zoomY)) → F61
  92. Text("x_" * B62 + "_" * A62 * "=", (x(A) + 1.7 * zoomX, y(A) - (B37 * 10 + A37) * 0.15 * zoomY)) → F62
  93. Text("x_" * B63 + "_" * A63 * "=", (x(A) + 1.7 * zoomX, y(A) - (B38 * 10 + A38) * 0.15 * zoomY)) → F63
  94. Text("x_" * B64 + "_" * A64 * "=", (x(A) + 1.7 * zoomX, y(A) - (B39 * 10 + A39) * 0.15 * zoomY)) → F64
  95. Text("x_" * B65 + "_" * A65 * "=", (x(A) + 1.7 * zoomX, y(A) - (B40 * 10 + A40) * 0.15 * zoomY)) → F65
  96. Text("x_" * B66 + "_" * A66 * "=", (x(A) + 1.7 * zoomX, y(A) - (B41 * 10 + A41) * 0.15 * zoomY)) → F66
  97. Text("x_" * B67 + "_" * A67 * "=", (x(A) + 1.7 * zoomX, y(A) - (B42 * 10 + A42) * 0.15 * zoomY)) → F67
  98. Text("x_" * B68 + "_" * A68 * "=", (x(A) + 1.7 * zoomX, y(A) - (B43 * 10 + A43) * 0.15 * zoomY)) → F68
  99. Text("x_" * B69 + "_" * A69 * "=", (x(A) + 1.7 * zoomX, y(A) - (B44 * 10 + A44) * 0.15 * zoomY)) → F69
  100. Text("x_" * B70 + "_" * A70 * "=", (x(A) + 1.7 * zoomX, y(A) - (B45 * 10 + A45) * 0.15 * zoomY)) → F70
  101. Text("x_" * B71 + "_" * A71 * "=", (x(A) + 1.7 * zoomX, y(A) - (B46 * 10 + A46) * 0.15 * zoomY)) → F71
  102. Text("x_" * B72 + "_" * A72 * "=", (x(A) + 1.7 * zoomX, y(A) - (B47 * 10 + A47) * 0.15 * zoomY)) → F72
  103. Text("x_" * B73 + "_" * A73 * "=", (x(A) + 1.7 * zoomX, y(A) - (B48 * 10 + A48) * 0.15 * zoomY)) → F73
  104. Text("x_" * B74 + "_" * A74 * "=", (x(A) + 1.7 * zoomX, y(A) - (B49 * 10 + A49) * 0.15 * zoomY)) → F74
  105. Text("x_" * B75 + "_" * A75 * "=", (x(A) + 1.7 * zoomX, y(A) - (B50 * 10 + A50) * 0.15 * zoomY)) → F75
  106. Text("x_" * B76 + "_" * A76 * "=", (x(A) + 1.7 * zoomX, y(A) - (B51 * 10 + A51) * 0.15 * zoomY)) → F76
  107. Text("x_" * B77 + "_" * A77 * "=", (x(A) + 1.7 * zoomX, y(A) - (B52 * 10 + A52) * 0.15 * zoomY)) → F77
  108. Text("x_" * B78 + "_" * A78 * "=", (x(A) + 1.7 * zoomX, y(A) - (B53 * 10 + A53) * 0.15 * zoomY)) → F78
  109. Text("x_" * B79 + "_" * A79 * "=", (x(A) + 1.7 * zoomX, y(A) - (B54 * 10 + A54) * 0.15 * zoomY)) → F79
  110. Text("x_" * B80 + "_" * A80 * "=", (x(A) + 1.7 * zoomX, y(A) - (B55 * 10 + A55) * 0.15 * zoomY)) → F80
  111. Text("x_" * B81 + "_" * A81 * "=", (x(A) + 1.7 * zoomX, y(A) - (B56 * 10 + A56) * 0.15 * zoomY)) → F81
  112. Text("x_" * B82 + "_" * A82 * "=", (x(A) + 1.7 * zoomX, y(A) - (B57 * 10 + A57) * 0.15 * zoomY)) → F82
  113. Text("x_" * B83 + "_" * A83 * "=", (x(A) + 1.7 * zoomX, y(A) - (B58 * 10 + A58) * 0.15 * zoomY)) → F83
  114. Text("x_" * B84 + "_" * A84 * "=", (x(A) + 1.7 * zoomX, y(A) - (B59 * 10 + A59) * 0.15 * zoomY)) → F84
  115. Text("x_" * B85 + "_" * A85 * "=", (x(A) + 1.7 * zoomX, y(A) - (B60 * 10 + A60) * 0.15 * zoomY)) → F85
  116. Text("x_" * B86 + "_" * A86 * "=", (x(A) + 1.7 * zoomX, y(A) - (B61 * 10 + A61) * 0.15 * zoomY)) → F86
  117. Text("x_" * B87 + "_" * A87 * "=", (x(A) + 1.7 * zoomX, y(A) - (B62 * 10 + A62) * 0.15 * zoomY)) → F87
  118. Text("x_" * B88 + "_" * A88 * "=", (x(A) + 1.7 * zoomX, y(A) - (B63 * 10 + A63) * 0.15 * zoomY)) → F88
  119. Text("x_" * B89 + "_" * A89 * "=", (x(A) + 1.7 * zoomX, y(A) - (B64 * 10 + A64) * 0.15 * zoomY)) → F89
  120. Text("x_" * B90 + "_" * A90 * "=", (x(A) + 1.7 * zoomX, y(A) - (B65 * 10 + A65) * 0.15 * zoomY)) → F90
  121. Text("x_" * B91 + "_" * A91 * "=", (x(A) + 1.7 * zoomX, y(A) - (B66 * 10 + A66) * 0.15 * zoomY)) → F91
  122. Text("x_" * B92 + "_" * A92 * "=", (x(A) + 1.7 * zoomX, y(A) - (B67 * 10 + A67) * 0.15 * zoomY)) → F92
  123. Text("x_" * B93 + "_" * A93 * "=", (x(A) + 1.7 * zoomX, y(A) - (B68 * 10 + A68) * 0.15 * zoomY)) → F93
  124. Text("x_" * B94 + "_" * A94 * "=", (x(A) + 1.7 * zoomX, y(A) - (B69 * 10 + A69) * 0.15 * zoomY)) → F94
  125. Text("x_" * B95 + "_" * A95 * "=", (x(A) + 1.7 * zoomX, y(A) - (B70 * 10 + A70) * 0.15 * zoomY)) → F95
  126. Text("x_" * B96 + "_" * A96 * "=", (x(A) + 1.7 * zoomX, y(A) - (B71 * 10 + A71) * 0.15 * zoomY)) → F96
  127. Text("x_" * B97 + "_" * A97 * "=", (x(A) + 1.7 * zoomX, y(A) - (B72 * 10 + A72) * 0.15 * zoomY)) → F97
  128. Text("x_" * B98 + "_" * A98 * "=", (x(A) + 1.7 * zoomX, y(A) - (B73 * 10 + A73) * 0.15 * zoomY)) → F98
  129. Text("x_" * B99 + "_" * A99 * "=", (x(A) + 1.7 * zoomX, y(A) - (B74 * 10 + A74) * 0.15 * zoomY)) → F99
  130. Text("x_" * B100 + "_" * A100 * "=", (x(A) + 1.7 * zoomX, y(A) - (B75 * 10 + A75) * 0.15 * zoomY)) → F100
  131. Text(C28, (x(A) + 2.1 * zoomX, y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → G28
  132. Text(C29, (x(A) + 2.1 * zoomX, y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → G29
  133. Text(C30, (x(A) + 2.1 * zoomX, y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → G30
  134. Text(C31, (x(A) + 2.1 * zoomX, y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → G31
  135. Text(C32, (x(A) + 2.1 * zoomX, y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → G32
  136. Text(C33, (x(A) + 2.1 * zoomX, y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → G33
  137. Text(C34, (x(A) + 2.1 * zoomX, y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → G34
  138. Text(C35, (x(A) + 2.1 * zoomX, y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → G35
  139. Text(C36, (x(A) + 2.1 * zoomX, y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → G36
  140. Text(C37, (x(A) + 2.1 * zoomX, y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → G37
  141. Text(C38, (x(A) + 2.1 * zoomX, y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → G38
  142. Text(C39, (x(A) + 2.1 * zoomX, y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → G39
  143. Text(C40, (x(A) + 2.1 * zoomX, y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → G40
  144. Text(C41, (x(A) + 2.1 * zoomX, y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → G41
  145. Text(C42, (x(A) + 2.1 * zoomX, y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → G42
  146. Text(C43, (x(A) + 2.1 * zoomX, y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → G43
  147. Text(C44, (x(A) + 2.1 * zoomX, y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → G44
  148. Text(C45, (x(A) + 2.1 * zoomX, y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → G45
  149. Text(C46, (x(A) + 2.1 * zoomX, y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → G46
  150. Text(C47, (x(A) + 2.1 * zoomX, y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → G47
  151. Text(C48, (x(A) + 2.1 * zoomX, y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → G48
  152. Text(C49, (x(A) + 2.1 * zoomX, y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → G49
  153. Text(C50, (x(A) + 2.1 * zoomX, y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → G50
  154. Text(C51, (x(A) + 2.1 * zoomX, y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → G51
  155. Text(C52, (x(A) + 2.1 * zoomX, y(A) - (B27 * 10 + A27) * 0.15 * zoomY)) → G52
  156. Text(C53, (x(A) + 2.1 * zoomX, y(A) - (B28 * 10 + A28) * 0.15 * zoomY)) → G53
  157. Text(C54, (x(A) + 2.1 * zoomX, y(A) - (B29 * 10 + A29) * 0.15 * zoomY)) → G54
  158. Text(C55, (x(A) + 2.1 * zoomX, y(A) - (B30 * 10 + A30) * 0.15 * zoomY)) → G55
  159. Text(C56, (x(A) + 2.1 * zoomX, y(A) - (B31 * 10 + A31) * 0.15 * zoomY)) → G56
  160. Text(C57, (x(A) + 2.1 * zoomX, y(A) - (B32 * 10 + A32) * 0.15 * zoomY)) → G57
  161. Text(C58, (x(A) + 2.1 * zoomX, y(A) - (B33 * 10 + A33) * 0.15 * zoomY)) → G58
  162. Text(C59, (x(A) + 2.1 * zoomX, y(A) - (B34 * 10 + A34) * 0.15 * zoomY)) → G59
  163. Text(C60, (x(A) + 2.1 * zoomX, y(A) - (B35 * 10 + A35) * 0.15 * zoomY)) → G60
  164. Text(C61, (x(A) + 2.1 * zoomX, y(A) - (B36 * 10 + A36) * 0.15 * zoomY)) → G61
  165. Text(C62, (x(A) + 2.1 * zoomX, y(A) - (B37 * 10 + A37) * 0.15 * zoomY)) → G62
  166. Text(C63, (x(A) + 2.1 * zoomX, y(A) - (B38 * 10 + A38) * 0.15 * zoomY)) → G63
  167. Text(C64, (x(A) + 2.1 * zoomX, y(A) - (B39 * 10 + A39) * 0.15 * zoomY)) → G64
  168. Text(C65, (x(A) + 2.1 * zoomX, y(A) - (B40 * 10 + A40) * 0.15 * zoomY)) → G65
  169. Text(C66, (x(A) + 2.1 * zoomX, y(A) - (B41 * 10 + A41) * 0.15 * zoomY)) → G66
  170. Text(C67, (x(A) + 2.1 * zoomX, y(A) - (B42 * 10 + A42) * 0.15 * zoomY)) → G67
  171. Text(C68, (x(A) + 2.1 * zoomX, y(A) - (B43 * 10 + A43) * 0.15 * zoomY)) → G68
  172. Text(C69, (x(A) + 2.1 * zoomX, y(A) - (B44 * 10 + A44) * 0.15 * zoomY)) → G69
  173. Text(C70, (x(A) + 2.1 * zoomX, y(A) - (B45 * 10 + A45) * 0.15 * zoomY)) → G70
  174. Text(C71, (x(A) + 2.1 * zoomX, y(A) - (B46 * 10 + A46) * 0.15 * zoomY)) → G71
  175. Text(C72, (x(A) + 2.1 * zoomX, y(A) - (B47 * 10 + A47) * 0.15 * zoomY)) → G72
  176. Text(C73, (x(A) + 2.1 * zoomX, y(A) - (B48 * 10 + A48) * 0.15 * zoomY)) → G73
  177. Text(C74, (x(A) + 2.1 * zoomX, y(A) - (B49 * 10 + A49) * 0.15 * zoomY)) → G74
  178. Text(C75, (x(A) + 2.1 * zoomX, y(A) - (B50 * 10 + A50) * 0.15 * zoomY)) → G75
  179. Text(C76, (x(A) + 2.1 * zoomX, y(A) - (B51 * 10 + A51) * 0.15 * zoomY)) → G76
  180. Text(C77, (x(A) + 2.1 * zoomX, y(A) - (B52 * 10 + A52) * 0.15 * zoomY)) → G77
  181. Text(C78, (x(A) + 2.1 * zoomX, y(A) - (B53 * 10 + A53) * 0.15 * zoomY)) → G78
  182. Text(C79, (x(A) + 2.1 * zoomX, y(A) - (B54 * 10 + A54) * 0.15 * zoomY)) → G79
  183. Text(C80, (x(A) + 2.1 * zoomX, y(A) - (B55 * 10 + A55) * 0.15 * zoomY)) → G80
  184. Text(C81, (x(A) + 2.1 * zoomX, y(A) - (B56 * 10 + A56) * 0.15 * zoomY)) → G81
  185. Text(C82, (x(A) + 2.1 * zoomX, y(A) - (B57 * 10 + A57) * 0.15 * zoomY)) → G82
  186. Text(C83, (x(A) + 2.1 * zoomX, y(A) - (B58 * 10 + A58) * 0.15 * zoomY)) → G83
  187. Text(C84, (x(A) + 2.1 * zoomX, y(A) - (B59 * 10 + A59) * 0.15 * zoomY)) → G84
  188. Text(C85, (x(A) + 2.1 * zoomX, y(A) - (B60 * 10 + A60) * 0.15 * zoomY)) → G85
  189. Text(C86, (x(A) + 2.1 * zoomX, y(A) - (B61 * 10 + A61) * 0.15 * zoomY)) → G86
  190. Text(C87, (x(A) + 2.1 * zoomX, y(A) - (B62 * 10 + A62) * 0.15 * zoomY)) → G87
  191. Text(C88, (x(A) + 2.1 * zoomX, y(A) - (B63 * 10 + A63) * 0.15 * zoomY)) → G88
  192. Text(C89, (x(A) + 2.1 * zoomX, y(A) - (B64 * 10 + A64) * 0.15 * zoomY)) → G89
  193. Text(C90, (x(A) + 2.1 * zoomX, y(A) - (B65 * 10 + A65) * 0.15 * zoomY)) → G90
  194. Text(C91, (x(A) + 2.1 * zoomX, y(A) - (B66 * 10 + A66) * 0.15 * zoomY)) → G91
  195. Text(C92, (x(A) + 2.1 * zoomX, y(A) - (B67 * 10 + A67) * 0.15 * zoomY)) → G92
  196. Text(C93, (x(A) + 2.1 * zoomX, y(A) - (B68 * 10 + A68) * 0.15 * zoomY)) → G93
  197. Text(C94, (x(A) + 2.1 * zoomX, y(A) - (B69 * 10 + A69) * 0.15 * zoomY)) → G94
  198. Text(C95, (x(A) + 2.1 * zoomX, y(A) - (B70 * 10 + A70) * 0.15 * zoomY)) → G95
  199. Text(C96, (x(A) + 2.1 * zoomX, y(A) - (B71 * 10 + A71) * 0.15 * zoomY)) → G96
  200. Text(C97, (x(A) + 2.1 * zoomX, y(A) - (B72 * 10 + A72) * 0.15 * zoomY)) → G97
  201. Text(C98, (x(A) + 2.1 * zoomX, y(A) - (B73 * 10 + A73) * 0.15 * zoomY)) → G98
  202. Text(C99, (x(A) + 2.1 * zoomX, y(A) - (B74 * 10 + A74) * 0.15 * zoomY)) → G99
  203. Text(C100, (x(A) + 2.1 * zoomX, y(A) - (B75 * 10 + A75) * 0.15 * zoomY)) → G100
  204. Segment((C1, C1), (C1, f(C1))) → D1
  205. Segment((C1, f(C1)), (C2, C2)) → E2
  206. Segment((C2, f(C2)), (C3, C3)) → E3
  207. Segment((C3, f(C3)), (C4, C4)) → E4
  208. Segment((C4, f(C4)), (C5, C5)) → E5
  209. Segment((C5, f(C5)), (C6, C6)) → E6
  210. Segment((C6, f(C6)), (C7, C7)) → E7
  211. Segment((C7, f(C7)), (C8, C8)) → E8
  212. Segment((C8, f(C8)), (C9, C9)) → E9
  213. Segment((C9, f(C9)), (C10, C10)) → E10
  214. Segment((C10, f(C10)), (C11, C11)) → E11
  215. Segment((C11, f(C11)), (C12, C12)) → E12
  216. Segment((C12, f(C12)), (C13, C13)) → E13
  217. Segment((C13, f(C13)), (C14, C14)) → E14
  218. Segment((C14, f(C14)), (C15, C15)) → E15
  219. Segment((C15, f(C15)), (C16, C16)) → E16
  220. Segment((C16, f(C16)), (C17, C17)) → E17
  221. Segment((C17, f(C17)), (C18, C18)) → E18
  222. Segment((C18, f(C18)), (C19, C19)) → E19
  223. Segment((C19, f(C19)), (C20, C20)) → E20
  224. Segment((C20, f(C20)), (C21, C21)) → E21
  225. Segment((C21, f(C21)), (C22, C22)) → E22
  226. Segment((C22, f(C22)), (C23, C23)) → E23
  227. Segment((C23, f(C23)), (C24, C24)) → E24
  228. Segment((C24, f(C24)), (C25, C25)) → E25
  229. Segment((C25, f(C25)), (C26, C26)) → E26
  230. Segment((C26, f(C26)), (C27, C27)) → E27
  231. Segment((C27, f(C27)), (C28, C28)) → E28
  232. Segment((C28, f(C28)), (C29, C29)) → E29
  233. Segment((C29, f(C29)), (C30, C30)) → E30
  234. Segment((C30, f(C30)), (C31, C31)) → E31
  235. Segment((C31, f(C31)), (C32, C32)) → E32
  236. Segment((C32, f(C32)), (C33, C33)) → E33
  237. Segment((C33, f(C33)), (C34, C34)) → E34
  238. Segment((C34, f(C34)), (C35, C35)) → E35
  239. Segment((C35, f(C35)), (C36, C36)) → E36
  240. Segment((C36, f(C36)), (C37, C37)) → E37
  241. Segment((C37, f(C37)), (C38, C38)) → E38
  242. Segment((C38, f(C38)), (C39, C39)) → E39
  243. Segment((C39, f(C39)), (C40, C40)) → E40
  244. Segment((C40, f(C40)), (C41, C41)) → E41
  245. Segment((C41, f(C41)), (C42, C42)) → E42
  246. Segment((C42, f(C42)), (C43, C43)) → E43
  247. Segment((C43, f(C43)), (C44, C44)) → E44
  248. Segment((C44, f(C44)), (C45, C45)) → E45
  249. Segment((C45, f(C45)), (C46, C46)) → E46
  250. Segment((C46, f(C46)), (C47, C47)) → E47
  251. Segment((C47, f(C47)), (C48, C48)) → E48
  252. Segment((C48, f(C48)), (C49, C49)) → E49
  253. Segment((C49, f(C49)), (C50, C50)) → E50
  254. Segment((C50, f(C50)), (C51, C51)) → E51
  255. Segment((C51, f(C51)), (C52, C52)) → E52
  256. Segment((C52, f(C52)), (C53, C53)) → E53
  257. Segment((C53, f(C53)), (C54, C54)) → E54
  258. Segment((C54, f(C54)), (C55, C55)) → E55
  259. Segment((C55, f(C55)), (C56, C56)) → E56
  260. Segment((C56, f(C56)), (C57, C57)) → E57
  261. Segment((C57, f(C57)), (C58, C58)) → E58
  262. Segment((C58, f(C58)), (C59, C59)) → E59
  263. Segment((C59, f(C59)), (C60, C60)) → E60
  264. Segment((C60, f(C60)), (C61, C61)) → E61
  265. Segment((C61, f(C61)), (C62, C62)) → E62
  266. Segment((C62, f(C62)), (C63, C63)) → E63
  267. Segment((C63, f(C63)), (C64, C64)) → E64
  268. Segment((C64, f(C64)), (C65, C65)) → E65
  269. Segment((C65, f(C65)), (C66, C66)) → E66
  270. Segment((C66, f(C66)), (C67, C67)) → E67
  271. Segment((C67, f(C67)), (C68, C68)) → E68
  272. Segment((C68, f(C68)), (C69, C69)) → E69
  273. Segment((C69, f(C69)), (C70, C70)) → E70
  274. Segment((C70, f(C70)), (C71, C71)) → E71
  275. Segment((C71, f(C71)), (C72, C72)) → E72
  276. Segment((C72, f(C72)), (C73, C73)) → E73
  277. Segment((C73, f(C73)), (C74, C74)) → E74
  278. Segment((C74, f(C74)), (C75, C75)) → E75
  279. Segment((C75, f(C75)), (C76, C76)) → E76
  280. Segment((C76, f(C76)), (C77, C77)) → E77
  281. Segment((C77, f(C77)), (C78, C78)) → E78
  282. Segment((C78, f(C78)), (C79, C79)) → E79
  283. Segment((C79, f(C79)), (C80, C80)) → E80
  284. Segment((C80, f(C80)), (C81, C81)) → E81
  285. Segment((C81, f(C81)), (C82, C82)) → E82
  286. Segment((C82, f(C82)), (C83, C83)) → E83
  287. Segment((C83, f(C83)), (C84, C84)) → E84
  288. Segment((C84, f(C84)), (C85, C85)) → E85
  289. Segment((C85, f(C85)), (C86, C86)) → E86
  290. Segment((C86, f(C86)), (C87, C87)) → E87
  291. Segment((C87, f(C87)), (C88, C88)) → E88
  292. Segment((C88, f(C88)), (C89, C89)) → E89
  293. Segment((C89, f(C89)), (C90, C90)) → E90
  294. Segment((C90, f(C90)), (C91, C91)) → E91
  295. Segment((C91, f(C91)), (C92, C92)) → E92
  296. Segment((C92, f(C92)), (C93, C93)) → E93
  297. Segment((C93, f(C93)), (C94, C94)) → E94
  298. Segment((C94, f(C94)), (C95, C95)) → E95
  299. Segment((C95, f(C95)), (C96, C96)) → E96
  300. Segment((C96, f(C96)), (C97, C97)) → E97
  301. Segment((C97, f(C97)), (C98, C98)) → E98
  302. Segment((C98, f(C98)), (C99, C99)) → E99
  303. Segment((C99, f(C99)), (C100, C100)) → E100
  304. Segment((C2, C2), (C2, f(C2))) → D2
  305. Segment((C3, C3), (C3, f(C3))) → D3
  306. Segment((C4, C4), (C4, f(C4))) → D4
  307. Segment((C5, C5), (C5, f(C5))) → D5
  308. Segment((C6, C6), (C6, f(C6))) → D6
  309. Segment((C7, C7), (C7, f(C7))) → D7
  310. Segment((C8, C8), (C8, f(C8))) → D8
  311. Segment((C9, C9), (C9, f(C9))) → D9
  312. Segment((C10, C10), (C10, f(C10))) → D10
  313. Segment((C11, C11), (C11, f(C11))) → D11
  314. Segment((C12, C12), (C12, f(C12))) → D12
  315. Segment((C13, C13), (C13, f(C13))) → D13
  316. Segment((C14, C14), (C14, f(C14))) → D14
  317. Segment((C15, C15), (C15, f(C15))) → D15
  318. Segment((C16, C16), (C16, f(C16))) → D16
  319. Segment((C17, C17), (C17, f(C17))) → D17
  320. Segment((C18, C18), (C18, f(C18))) → D18
  321. Segment((C19, C19), (C19, f(C19))) → D19
  322. Segment((C20, C20), (C20, f(C20))) → D20
  323. Segment((C21, C21), (C21, f(C21))) → D21
  324. Segment((C22, C22), (C22, f(C22))) → D22
  325. Segment((C23, C23), (C23, f(C23))) → D23
  326. Segment((C24, C24), (C24, f(C24))) → D24
  327. Segment((C25, C25), (C25, f(C25))) → D25
  328. Segment((C26, C26), (C26, f(C26))) → D26
  329. Segment((C27, C27), (C27, f(C27))) → D27
  330. Segment((C28, C28), (C28, f(C28))) → D28
  331. Segment((C29, C29), (C29, f(C29))) → D29
  332. Segment((C30, C30), (C30, f(C30))) → D30
  333. Segment((C31, C31), (C31, f(C31))) → D31
  334. Segment((C32, C32), (C32, f(C32))) → D32
  335. Segment((C33, C33), (C33, f(C33))) → D33
  336. Segment((C34, C34), (C34, f(C34))) → D34
  337. Segment((C35, C35), (C35, f(C35))) → D35
  338. Segment((C36, C36), (C36, f(C36))) → D36
  339. Segment((C37, C37), (C37, f(C37))) → D37
  340. Segment((C38, C38), (C38, f(C38))) → D38
  341. Segment((C39, C39), (C39, f(C39))) → D39
  342. Segment((C40, C40), (C40, f(C40))) → D40
  343. Segment((C41, C41), (C41, f(C41))) → D41
  344. Segment((C42, C42), (C42, f(C42))) → D42
  345. Segment((C43, C43), (C43, f(C43))) → D43
  346. Segment((C44, C44), (C44, f(C44))) → D44
  347. Segment((C45, C45), (C45, f(C45))) → D45
  348. Segment((C46, C46), (C46, f(C46))) → D46
  349. Segment((C47, C47), (C47, f(C47))) → D47
  350. Segment((C48, C48), (C48, f(C48))) → D48
  351. Segment((C49, C49), (C49, f(C49))) → D49
  352. Segment((C50, C50), (C50, f(C50))) → D50
  353. Segment((C51, C51), (C51, f(C51))) → D51
  354. Segment((C52, C52), (C52, f(C52))) → D52
  355. Segment((C53, C53), (C53, f(C53))) → D53
  356. Segment((C54, C54), (C54, f(C54))) → D54
  357. Segment((C55, C55), (C55, f(C55))) → D55
  358. Segment((C56, C56), (C56, f(C56))) → D56
  359. Segment((C57, C57), (C57, f(C57))) → D57
  360. Segment((C58, C58), (C58, f(C58))) → D58
  361. Segment((C59, C59), (C59, f(C59))) → D59
  362. Segment((C60, C60), (C60, f(C60))) → D60
  363. Segment((C61, C61), (C61, f(C61))) → D61
  364. Segment((C62, C62), (C62, f(C62))) → D62
  365. Segment((C63, C63), (C63, f(C63))) → D63
  366. Segment((C64, C64), (C64, f(C64))) → D64
  367. Segment((C65, C65), (C65, f(C65))) → D65
  368. Segment((C66, C66), (C66, f(C66))) → D66
  369. Segment((C67, C67), (C67, f(C67))) → D67
  370. Segment((C68, C68), (C68, f(C68))) → D68
  371. Segment((C69, C69), (C69, f(C69))) → D69
  372. Segment((C70, C70), (C70, f(C70))) → D70
  373. Segment((C71, C71), (C71, f(C71))) → D71
  374. Segment((C72, C72), (C72, f(C72))) → D72
  375. Segment((C73, C73), (C73, f(C73))) → D73
  376. Segment((C74, C74), (C74, f(C74))) → D74
  377. Segment((C75, C75), (C75, f(C75))) → D75
  378. Segment((C76, C76), (C76, f(C76))) → D76
  379. Segment((C77, C77), (C77, f(C77))) → D77
  380. Segment((C78, C78), (C78, f(C78))) → D78
  381. Segment((C79, C79), (C79, f(C79))) → D79
  382. Segment((C80, C80), (C80, f(C80))) → D80
  383. Segment((C81, C81), (C81, f(C81))) → D81
  384. Segment((C82, C82), (C82, f(C82))) → D82
  385. Segment((C83, C83), (C83, f(C83))) → D83
  386. Segment((C84, C84), (C84, f(C84))) → D84
  387. Segment((C85, C85), (C85, f(C85))) → D85
  388. Segment((C86, C86), (C86, f(C86))) → D86
  389. Segment((C87, C87), (C87, f(C87))) → D87
  390. Segment((C88, C88), (C88, f(C88))) → D88
  391. Segment((C89, C89), (C89, f(C89))) → D89
  392. Segment((C90, C90), (C90, f(C90))) → D90
  393. Segment((C91, C91), (C91, f(C91))) → D91
  394. Segment((C92, C92), (C92, f(C92))) → D92
  395. Segment((C93, C93), (C93, f(C93))) → D93
  396. Segment((C94, C94), (C94, f(C94))) → D94
  397. Segment((C95, C95), (C95, f(C95))) → D95
  398. Segment((C96, C96), (C96, f(C96))) → D96
  399. Segment((C97, C97), (C97, f(C97))) → D97
  400. Segment((C98, C98), (C98, f(C98))) → D98
  401. Segment((C99, C99), (C99, f(C99))) → D99
  402. Segment((C100, C100), (C100, f(C100))) → D100

AI Drawing Prompt Reference

Draw a function graph and illustrate the iteration process by rearranging the equation into x=g(x). First, plot the function f(x) and its derivative f'(x), then mark the initial point x_0 on the x-axis. Calculate and plot subsequent iteration points using the formula x_{n+1}=g(x_n), label each point's coordinates with text, and connect adjacent points with line segments to show the convergence of the iteration sequence.
The prompt above was compiled from the original drawing commands and is for reference only.