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Individual task in calculus 4 October 2018.
Edited at 4pm 4 October 2018.
s is your student number.
k = s mod 10000. T = s mod 100. m10= s mod 10.
T = 1. When does limit exist?
T = 2. List indeterminate forms.
T = 3. What the properties of the limit? (times constant, sum, product, quotient)
T = 4. Give the main methods for calculating limits.
T = 5. What are the great limits of calculus? 1. 2.
T = 6. [pic]=
T = 7. [pic]
T = 8. [pic] =
T = 9. [pic]
T = 10. [pic]
T = 11. [pic]
T = 12. [pic]
T = 13. [pic]
Use
Continuity:
Investigate continuity of the function:
T = 14. x
T = 15. [pic]
T = 16. [pic]
T = 17. [pic]
T = 18. [pic]
T = 19. [pic]
T = 20. [pic]
Derivative:
T = 21. Give the properties of derivative: times constant, sum, product, quotient.
T = 22. Prove expression for derivative of x2 using limit.
Find derivatives of these functions:
T = 23. ex
T = 24. xp
T = 25. cos(x)
T = 26. [pic]
Applications of derivatives:
Increasing or decreasing:
T = 27. -6x
T = 28. 9x
T = 29. sin(x)
T = 30. cos(x)
T = 31. tan(x)
Theorems:
T = 32. What is Mean Value Theorem?
T = 33. Explain Rolle theorem.
T = 34. Give Fermat theorem.
(stationary_points)
Concave or convex:
T = 35. x3
T = 36.-x3
T = 37. cos(x)
T = 38. sin(x)
Find inflection point:
T = 39. x3
T = 40.-x3
m10 = 1: 41. cos(x)
m10 = 2: 42. sin(x)
m10 = 3: 43. What is curvature?
m10 = 4: 44. Explain linear approximation.
m10 = 5: 45. What is chain rule?
Multivariate derivatives:
Calculate partial derivatives of the function:
m10 = 6: 46. xy
m10 = 7: 47. yz
m10 = 8: 48. xz
m10 = 9: 49. xyz
m10 = 0: 50. Find linear least-square approximation for your dataset.
51. Calculate (1 + 1/T)T.
52. [pic]. f(x) = Tx + k. For any ε find δ, using ε – δ definition of the limit.
Find derivatives of these functions:
53. xT.
54. sin Tx
55. Find the largest area rectangle with perimeter of T meters.
56. Calculate the largest area right-angled triangle with perimeter of T meters.
57. Find maximum volume cylinder for surface area of T meters square.
58. Calculate maximum volume cone for surface area of T meters square.
59. Calculate maximum area scalene triangle with perimeter of T meters.
60. Find the best song using calculus.
Other October tasks:
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