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group task in calculus 4 October 2018.Edited at 4pm 4 October 2018.Limit: 1. When does limit exist?. List indeterminate forms.. What the properties of the limit? (times constant, sum, product, quotient)4. Give the main methods for calculating limits. 5. What are the great limits of calculus? 1. 2. 6. Limn→∞sinn =7. Limx→0sin1x=8. Limx→0x =9. Limx→01x=10. Limx→01x2=11. Limx→0xx=12. Limx→1x2-3x+2x-1=13. Limx→2x2-3x+2x-2=Use: Investigate continuity of the function:14. x15. x16. 1x17. 1x218. xx19. x2-3x+2x-120. x2-3x+2x-2Derivative:21. Give the properties of derivative: times constant, sum, product, quotient. 22. Prove expression for derivative of x2 using limit. Find derivatives of these functions:23. ex24. xp25. cos(x)26. xnn of derivatives:Increasing or decreasing: 27. -6x28. 9x29. sin(x)30. cos(x)31. tan(x)Theorems: 32. What is Mean Value Theorem? . Explain Rolle theorem.. Give Fermat theorem. (stationary_points)Concave or convex:35. x336.-x337. cos(x)38. sin(x)Find inflection point:39. x340.-x341. cos(x)42. sin(x)43. What is curvature? . Explain linear approximation. . What is chain rule? derivatives: Calculate partial derivatives of the function:46. xy47. yz48. xz49. xyz50. Find linear least-square approximation for your dataset. 51. Calculate (1 + 1/999999999)999999999.52. Limx→pfx = L. f(x) = 99x + 9999. For any ε find δ, using ε – δ definition of the limit.Find derivatives of these functions:53. x99.54. sin 99x55. Find the largest area rectangle with perimeter of 99 meters.56. Calculate the largest area right-angled triangle with perimeter of 99 meters.57. Find maximum volume cylinder for surface area of 99 meters square.58. Calculate maximum volume cone for surface area of 99 meters square.59. Calculate maximum area scalene triangle with perimeter of 99 meters. 60. Find the best song using calculus. Other October tasks: ................
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