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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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