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Notes in calculus:Edited at 8am 28.9.2019.These notes are to help you in solving task. s is your student number.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.Answer all these questions the best you can. Deadline is 30.9.2019. ................
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