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2 individual task in calculus 26.10.2018.
October task (individual).
Edited at 8am 26.10.2018.
s is your student number.
Write your student number: s = ___________________
Write your name ___________________
k = s mod 10000. T = s mod 100.
m10 = s mod 10. m9 = s mod 9. m8 = s mod 8. m7 = s mod 7. m6 = s mod 6.
m5 = s mod 5. m4 = s mod 4. m3 = s mod 3. m2 = s mod 2.
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1 section:
Introduction to calculus:
1. Why do you need calculus?
Numbers:
2. Is 1/s a recurring decimal, why?
3. m3 = 0: Write 0.(742) as ratio.
4. m3 = 1: Write 2/7 as decimal.
5. m3 = 2: Write e as decimal
Functions:
6. m2 = 0: Give examples of algebraic functions.
7. m2 = 1: Give examples of transcendental functions.
8. Find the composite function f(g(x)), g(f(x)), f(f(x)), g(g(x)) for f (x) = kx, g(x) = Tx.
9. Find inverse function f-1(x) for f(x) = Tx + k.
10. m2 = 0: Find f(f-1(x)).
11. m2 = 1: Find f-1(f (x)).
Fractal:
12. Draw the Koch snowflake fractal for your student number for T iterations:
Dota2
13. Try to prepare to Dota2 gaming competition:
2019 Asia Soccer Cup:
14. Predict 2019 Asia Soccer Cup results.
Elections:
15. Predict results of Indonesian elections.
16. Calculate ratings of Jokowi and Prabowo T days after 31.10.2018.
International community:
17. Try to apply for all scholarships, fellowships, grants, etc. in North America, European Union, Japan, Australia, etc.
Tsunami:
18. How can we prevent bad consequences of tsunamis?
Project:
19. Write about your project.
20. Apply for American citizenship in October of 2018.
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2 section:
T = 1. 21. When does limit exist?
T = 2. 22. List indeterminate forms.
T = 3. 23. What the properties of the limit? (times constant, sum, product, quotient)
T = 4. 24. Give the main methods for calculating limits.
T = 5. 25. What are the great limits of calculus? 1. 2.
T = 6. 26. [pic]=
T = 7. 27. [pic]
T = 8. 28. [pic] =
T = 9. 29. [pic]
T = 10. 30. [pic]
T = 11. 31. [pic]
T = 12. 32. [pic]
T = 13. 33. [pic]
Use
Continuity:
Investigate continuity of the function:
T = 14. 34. x
T = 15. 35. [pic]
T = 16. 36. [pic]
T = 17. 37. [pic]
T = 18. 38. [pic]
T = 19. 39. [pic]
T = 20. 40. [pic]
Derivative:
T = 21. 41. Give the properties of derivative: times constant, sum, product, quotient.
T = 22. 42. Prove expression for derivative of x2 using limit.
Find derivatives of these functions:
T = 23. 43. ex
T = 24. 44. xp
T = 25. 45. cos(x)
T = 26. 46. [pic]
Applications of derivatives:
Increasing or decreasing:
T = 27. 47. -6x
T = 28. 48. 9x
T = 29. 49. sin(x)
T = 30. 50. cos(x)
T = 31. 51. tan(x)
Theorems:
T = 32. 52. What is Mean Value Theorem?
T = 33. 53. Explain Rolle theorem.
T = 34. 54. Give Fermat theorem.
(stationary_points)
Concave or convex:
T = 35. 55. x3
T = 36. 56. -x3
T = 37. 57. cos(x)
T = 38. 58. sin(x)
Find inflection point:
T = 39. 59. x3
T = 40. 60. -x3
m10 = 1: 61. cos(x)
m10 = 2: 62. sin(x)
m10 = 3: 63. What is curvature?
m10 = 4: 64. Explain linear approximation.
m10 = 5: 65. What is chain rule?
Multivariate derivatives:
Calculate partial derivatives of the function:
m10 = 6: 66. xy
m10 = 7: 67. yz
m10 = 8: 68. xz
m10 = 9: 69. xyz
m10 = 0: 70. Find linear least-square approximation for your dataset.
(2, m2), (3, m3), (4, m4)
Dim x(3), y(3)
m = 3
x(1) = 2
x(2) = 3
x(3) = 4
y(1) = 0
y(2) = 0
y(3) = 3
sx = 0
For j = 1 To m
sx = sx + x(j)
Next j
sy = 0
For j = 1 To m
sy = sy + y(j)
Next j
sxy = 0
For j = 1 To m
sxy = sxy + x(j) * y(j)
Next j
sx2 = 0
For j = 1 To m
sx2 = sx2 + x(j) ^ 2
Next j
g = (m * sxy - sx * sy) / (m * sx2 - sx ^ 2)
i = (sy - g * sx) / m
MsgBox g
MsgBox i
End Sub
71. Calculate (1 + 1/T)T.
72. [pic]. f(x) = Tx + k. For any ε find δ, using ε – δ definition of the limit.
Find derivatives of these functions:
73. xT.
74. sin Tx
75. Find the largest area rectangle with perimeter of T meters.
76. Calculate the largest area right-angled triangle with perimeter of T meters.
77. Find maximum volume cylinder for surface area of T meters square.
78. Calculate maximum volume cone for surface area of T meters square.
79. Calculate maximum area scalene triangle with perimeter of T meters.
80. Find the best song using calculus.
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3 section:
m10= 1. 81. Prove First Great Limit.
[pic]
Calculate Tsin(1/T).
m10= 2. 82. What is L’Hopital’s Rule?
m10= 3. 83. Calculate the limits using L’Hopital’s Rule.
[pic]
[pic]
[pic]
m10= 4. 84. Give types of discontinuity.
m10= 5. 85. Investigate linear function. L(x) = gx + i.
m10= 6. 86. Explain total derivative.
m10= 7. 87. What is inverse function derivative?
m10= 8. 88. Give implicit function derivative.
m10= 9. 89. Explore Zimmermann calculus competition.
m10= 0: 90. Predict 2018 USA elections results.
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4 section:
m10 = 1. 91. What is differential?
m10 = 2. 92. Explain vector.
m10 = 3. 93. What is vector calculus?
Define dot-product and cross-product of vectors.
m10 = 4. 94. Explain directional derivative.
m10 = 5. 95. What are div, curl, grad?
m10 = 6. 96. Explain differential equation.
Define integral.
m10 = 7. 97. Explain antiderivative?
m10 = 8. 98. What is Riemann sum?
m10 = 9. 99. Define functional series.
m10 = 0: 100. What are the main differences between differential and integral?
101. How can Indonesia avoid violence?
102. Solve number puzzle for m8 + 3 digits.
103. Hack password.
104. Find the discriminant of the elliptic curve y2 = x3 + Lx + T.
Here L = m10.
105. Why did Jamal Khashoggi disappear?
Use whiteboard pictures:
Use notes:
Deadline is 31.10.2018.
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