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2 group task in calculus 26.10.2018October task (group). Edited at 8am 26.10.2017.1 section: Numbers:1. What is a recurring decimal?2. Write 0.(742) as ratio.3. Write 2/7 as decimal.4. Write e as decimal5. Are there more or less irrational numbers than rational + integers + natural numbers? Why?6. Give examples of natural, integer, rational, irrational, real, and complex numbers.Functions:7. What is a function?8. Give examples of algebraic functions.9. Give examples of transcendental functions.10. Find f(f-1(x)).11. Find f-1(f (x)).Limit: 12. Find the limits of the functions.Continuity: 13. Show example of continuity. Fractal:14. What is fractal?. Try to prepare to Dota2 gaming competition: Asia Soccer Cup:16. Predict 2019 Asia Soccer Cup results. : 17. Predict results of Indonesian elections.18. Calculate ratings of Jokowi and Prabowo 50 days after 31.10.2018.: 19. Try to apply for all scholarships, fellowships, grants, etc. in North America, European Union, Japan, Australia, etc.Tsunami:20. How can we prevent bad consequences of tsunamis? -2 section: Limit: 21. When does limit exist?. List indeterminate forms.. What the properties of the limit? (times constant, sum, product, quotient)24. Give the main methods for calculating limits. 25. What are the great limits of calculus? 1. 2. 26. Limn→∞sinn =27. Limx→0sin1x=28. Limx→0x =29. Limx→01x=30. Limx→01x2=31. Limx→0xx=32. Limx→1x2-3x+2x-1=33. Limx→2x2-3x+2x-2=Use: Investigate continuity of the function:34. x35. x36. 1x37. 1x238. xx39. x2-3x+2x-140. x2-3x+2x-2Derivative:41. Give the properties of derivative: times constant, sum, product, quotient. 42. Prove expression for derivative of x2 using limit. Find derivatives of these functions:43. ex44. xp45. cos(x)46. xnn of derivatives:Increasing or decreasing: 47. -6x48. 9x49. sin(x)50. cos(x)51. tan(x)Theorems: 52. What is Mean Value Theorem? . Explain Rolle theorem.. Give Fermat theorem. (stationary_points)Concave or convex:55. x356.-x357. cos(x)58. sin(x)Find inflection point:59. x360.-x361. cos(x)62. sin(x)63. What is curvature? . Explain linear approximation. . What is chain rule? derivatives: Calculate partial derivatives of the function:66. xy67. yz68. xz69. xyz70. Find linear least-square approximation for your dataset. (46, 21), (17, 63), (26, 11) x(3), y(3)m = 3x(1) = 46x(2) = 17x(3) = 26y(1) = 21y(2) = 63y(3) = 11sx = 0For j = 1 To msx = sx + x(j)Next jsy = 0For j = 1 To msy = sy + y(j)Next jsxy = 0For j = 1 To msxy = sxy + x(j) * y(j)Next jsx2 = 0For j = 1 To msx2 = sx2 + x(j) ^ 2Next jg = (m * sxy - sx * sy) / (m * sx2 - sx ^ 2)i = (sy - g * sx) / mMsgBox gMsgBox iEnd Sub71. Calculate (1 + 1/999999999)999999999.72. Limx→pfx = L. f(x) = 99x + 9999. For any ε find δ, using ε – δ definition of the limit.Find derivatives of these functions:73. x99.74. sin 99x75. Find the largest area rectangle with perimeter of 99 meters.76. Calculate the largest area right-angled triangle with perimeter of 99 meters.77. Find maximum volume cylinder for surface area of 99 meters square.78. Calculate maximum volume cone for surface area of 99 meters square.79. Calculate maximum area scalene triangle with perimeter of 99 meters. 80. Find the best song using calculus. -3 section: 81. Prove First Great Limit. Limx→0sinxxCalculate 99sin(1/99).82. What is L’Hopital’s Rule?. Calculate the limits using L’Hopital’s Rule.Limx→0xx=Limx→1x2-3x+2x-1=Limx→2x2-3x+2x-2=84. Give types of discontinuity. 85. Investigate linear function. L(x) = gx + i.. Explain total derivative.. What is inverse function derivative?. Give implicit function derivative. . Explore Zimmermann calculus competition.. Predict 2018 USA elections results. section:91. What is differential?92. Explain vector. 93. What is vector calculus? dot-product and cross-product of vectors.94. Explain directional derivative.95. What are div, curl, grad?96. Explain differential equation.Define integral.97. Explain antiderivative?. What is Riemann sum?. Define functional series.100. What are the main differences between differential and integral?101. How can Indonesia avoid violence?. Solve number puzzle for 10 digits. . Hack password. . Find the discriminant of the elliptic curve y2 = x3 + 3x + 2.. Apply for American citizenship in October of 2018. whiteboard pictures: notes: is 31.10.2018. ................
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