Calculus17.weebly.com
Notes in calculus:Edited at 1pm 16.10.2019.These notes are to help you in solving task. s is your student number.For group task s = 19107089.k = s mod 10000. T = s mod 100. m35 = s mod 35. m25 = s mod 25. m20 = s mod 20. 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 2.1. Why do you need calculus?I need calculus because it is my job, the easiest of all subjects and very helpful in physics, chemistry, biology, and economics. 2. Find average of m2, m3, m4, and m5.This is the most important in math and science. 3. Which English letter is the thickest?4. Find maximum area rectangle for the same perimeter. Use your intuition. 5. What plane shape has maximum area for same perimeter?Use your intuition. 6. What is function?(mathematics)7. Do your project. Choose topic and write research paper about it.8. What is calculus of social media? Predict numerical characteristics of people and robots in social media.9. Study calculus of songs. Try to understand why some songs are popular, using calculus (sounds, frequencies, loudness, lyrics, etc.).10. Solve Zimmermann problem: for m20 + 6.Improve these solutions: you cannot register here then submit your solutions to me.Try to calculate the best solution of Zimmermann problem.11. What is fractal? often use fractals in computer science, computer graphics, computer security, etc.12. Explain least-squares fit. use least-squares fit to forecast. 13. Apply for American citizenship: . Apply for scholarships, grants, fellowships of USA, Europe, Canada, Australia, Japan, etc. 15. Study to find something interesting on these web sites.16. What is infinitely small value? small value is the most important in calculus. 17. Explain continuity. is the most important in calculus.18. Discuss calculus news.Choose any news, that you are interested in and try to analyze then using calculus.(2015%E2%80%93present). Study general concepts of limit, continuity, derivative, integral, differential equation, partial derivative, and optimization. (mathematics). How is calculus used in computer science?Cryptography, design of computers, chaotic irrational numbers, etc.-2 section: 21. Calculate limits: m8 = 0: Limn→∞sinn =m8 = 1: Limx→0sin1x=m8 = 2: Limx→0x =m8 = 3: Limx→01x=m8 = 4: Limx→01x2=m8 = 5: Limx→0xx=m8 = 6: Limx→1x2-3x+2x-1=m8 = 7: Limx→2x2-3x+2x-2=Use = 0: 22. When does limit exist? = 1: 23. List indeterminate forms.. Explain drone calculus. = 1: 25. What the properties of the limit? (times constant, sum, product, quotient)m2 = 0: 26. Give the main methods for calculating limits. 27. Prepare to Dota2 gaming competition:. What is chaos?. What are the great limits of calculus? 1. 2. 30. Investigate continuity of the function:m7 = 0: xm7 = 1: xm7 = 2: 1xm7 = 3: 1x2m7 = 4: xxm7 = 5: x2-3x+2x-1m7 = 6: x2-3x+2x-2m2 = 1: 31. Give the properties of derivative: times constant, sum, product, quotient. m2 = 0: 32. Prove expression for derivative of x2 using limit. 33. Find derivatives of these functions:m4 = 0: exm4 = 1: xpm4 = 2: cos(x)m4 = 3: xnn. Increasing or decreasing: m5 = 0: -6xm5 = 1: 9xm5 = 2: sin(x)m5 = 3: cos(x)m5 = 4: tan(x) is when derivative > 0.decrease is when derivative < 0.m3 = 0: 35. What is Mean Value Theorem? = 1: 36. Explain Rolle theorem. = 2: 37. Give Fermat theorem. (stationary_points)38. Concave or convex:m4 = 0: x3m4 = 1: -x3m4 = 2: cos(x)m4 = 3: sin(x) up is is when second derivative < 0.concave up is is when second derivative > 0.39. Find inflection point:m4 = 0: x3m4 = 1: -x3m4 = 2: cos(x)m4 = 3: sin(x) is when second derivative = 0.40. Enjoy calculus.-3 section: 41. Find min and Max.Find the largest area rectangle with perimeter of T meters.Calculate the largest area right-angled triangle with perimeter of T meters.Find maximum volume cylinder for surface area of T meters square.Calculate maximum volume cone for surface area of T meters square.Calculate maximum area scalene triangle with perimeter of T meters. Use derivative to find min and Max.42. How does guitar string move?We answered this on 2 October 2019.43. Explain power pyramid: USA, UK, EU, Australia, New Zealand, Japan, Korea, Singapore, Malaysia, Indonesia, China, India, Russia, etc.We answered this on 2 October 2019.44. Why are some civilizations more successful than the others?We answered this on 2 October 2019.45. Why are some people very massive?We answered this on 2 October 2019.46. What are Brownian motion, random walk and how are they linked to Zimmermann problem?We answered this on 2 October 2019.47. Predict results of 2019 rugby world cup: answered this on 2 October 2019.48. Explain good country index. answered this on 2 October 2019.49. Calculate (1+1/T)T. close is this to e?50. Solve number puzzle for 3 + m8 digits. answered this on 2 October 2019.51. Hack password. answered this on 2 October 2019.52. Why can crazy people be good for calculus?Craziness may find unusual solutionWe answered this on 2 October 2019.53. Who is internet troll?We answered this on 2 October 2019.54. Analyze these topics: answered this on 2 October 2019.55. Why is there less freedom in the world?Think of communism collapse in Europe.We answered this on 2 October 2019.56. Will Trump be impeached? Why?Count number of impeachments in USA.We answered this on 2 October 2019.57. How do we help Indonesia?We answered this on 2 October 2019.58. Limx→pfx = L. f(x) = Tx + k. For any ε find δ, using ε – δ definition of the limit.59. Find the discriminant of the elliptic curve y2 = x3 + Lx + T.Here L = m10. is for cryptography and cryptoanalysis.60. Find linear least-square approximation for your dataset. (2, m2), (3, m3), (4, m4) derivative to find min.-4 section:61. Why is there terror? Why is monopoly bad?Freedom solves many problems. Balance of powers in necessary for freedom. 62. Explain physics Nobel Prize 2019.Search information about physics Nobel Prize 2019.63. Do Bernoulli experiment.Blow bellow the paper, placed on top of the books and explain the result. 64. Find the hangover for the s blocks in the blocks stacking problem. statics to find the balance and show that it is half of harmonic series. 65. Use 3T mod n to pass secret.Calculate 3T mod 19 and exchange secret information with your friend. function produces almost perfect chaos, which allows people to protect their passwords well. 66. Calculate the largest prime number. largest prime number is necessary to improve safety of password. 67. Do prime factorization of s. factorization is used for password. -68. (xx)' = Use Ln to calculate this derivative or . Calculate derivative, using Chain Rule for sin(Tx). Find partial derivatives. m2 = 0: x + ym2 = 1: xy71. Calculate total derivative.m2 = 0: x + ym2 = 1: xy72. Find implicit function derivative. Lx2 + Ty2 – k = 0Sometimes it is hard or impossible to resolve function with respect to y. Such function is implicit. 73. Calculate inverse function derivative y = Tx + L.74. Analyze y = Tx + L. Find gradient, intercept, derivative, parallel line, perpendicular line. Straight line is among the most important concepts of calculus because derivative is linear approximation.75. Explainm8 = 0: composite functionm8 = 1: inverse functionm8 = 2: implicit functionm8 = 3: algebraic functionm8 = 4: transcendental functionm8 = 5: special functionm8 = 6: exponential functionm8 = 7: logarithmic functionThis is theory of functions. 76. Explainm6 = 0: natural numberm6 = 1: integerm6 = 2: rational numberm6 = 3: irrational numberm6 = 4: real numberm6 = 5: complex numberThis is number theory. 77. Give Fundamental Theorem of Calculus. Theorem of Calculus is the most important in calculus. 78. Integrate.xTdxsinTx dx01xTdx01sinTxdx. eTxdx80. 01eTxdx calculus is about integrals. Answer all these questions the best you can. Deadline is 20.10.2019. ................
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