Limits 1a - Definition and Basic Concepts 
Limits 1a - Definition and Basic Concepts
by Robert Donley
Video Lecture 1 of 82
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Date Added: April 4, 2016

Lecture Description

Calculus: We define the notion of a limit and interpret it both numerically and pictorially. We compute the examples (a) lim_{x_1} (x^2-1)/(x-1) and (b) lim_{x_2} (x^2-6x+8)/(x^2-5x+6). We also note an important trick for multiple choice exams.

Course Index

  1. Limits 1a - Definition and Basic Concepts
  2. Limits 1b - Delta-Epsilon Formulation
  3. Limits 1c - Limit Failure
  4. Limits 1d - Polynomial and Rational Functions
  5. Limits 1e - Compositions and Squeeze Theorem
  6. Limits 1f - Trigonometric Functions
  7. Examples of Limits
  8. Continuity 1a - Definition and Basic Concepts
  9. Continuity 1b - Polynomial/Rational Functions and The Extreme Value Theorem
  10. Examples of Continuity
  11. Fast Solution of Inequality Using Continuity
  12. Bisection Method 1
  13. Bisection Method 2
  14. Vertical Asymptotes 1a
  15. Vertical Asymptotes 1b
  16. Definition of Tangent Line
  17. Example of Tangent Line
  18. Definition of Derivative
  19. Power Rule for Derivatives
  20. Tangent Line to x^2-4x
  21. Horizontal Tangent Lines to a Polynomial
  22. Derivative of sin(x) and cos(x)
  23. Tangent Lines to sin(x)
  24. Motion in a Line
  25. The Product Rule
  26. General Product Rule
  27. Power Rule for Rational Exponents
  28. The Quotient Rule
  29. Trig Derivatives
  30. Examples of Trig Derivatives
  31. Tangent Lines for sec(x)
  32. Tangent Lines for cot(x)
  33. The Chain Rule
  34. Example of Chain Rule 1 - Basic Examples
  35. Example of Chain Rule 2 - Approximation with Tangent Line
  36. Example of Chain Rule 3 - Trig Functions
  37. Example of Chain Rule 4 - Triple Chain Rule
  38. Higher Order Derivatives
  39. Graphs and Higher Order Derivatives
  40. Implicit Differentiation 1 - Definition and Basic Concepts
  41. Implicit Differentiation 2 - Basic Example
  42. Implicit Differentiation 3 - Approximation with Tangent Line
  43. Implicit Differentiation 4 - Example with Trig Functions
  44. Implicit Differentiation 5 - Higher Derivatives
  45. Related Rates
  46. Example of Related Rates 1
  47. Example of Related Rates 2
  48. Extreme Value Theorem Using Critical Points
  49. Example of Extreme Value Theorem 1
  50. Example of Extreme Value Theorem 2
  51. Example of Extreme Value Theorem 3
  52. Rolle's Theorem
  53. Mean Value Theorem
  54. Increasing/Decreasing and Derivatives 1
  55. Increasing/Decreasing and Derivatives 2
  56. Example of Increasing/Decreasing 1
  57. Example of Increasing/Decreasing 2
  58. Example of Increasing/Decreasing 3
  59. First/Second Derivative Test for f(x) = x^4 - 12x^3
  60. First/Second Derivative Test for f(x) = sin(x)
  61. First/Second Derivative Test for f(x) = x^2 - 6x^{4/3}
  62. Concavity and the Second Derivative
  63. Concavity for f(x) = sin(x)
  64. Concavity for f(x) = (x^2 - 36)/(x-2)
  65. Concavity for f(x) = |x^2 - 4x - 12|
  66. Example of Limit at Infinity 1
  67. Example of Limit at Infinity 2
  68. Example of Limit at Infinity 3
  69. Checklist for Sketching Functions
  70. Graph of f(x) = x^4 - 8x^3
  71. Graph of f(x) = (x-2)/(x-1)
  72. Graph of f(x) = sin(x) + cos(x)
  73. Graph of f(x) = sin(x)/(1+cos(x))
  74. Graph of f(x) = x^{4/3} - 8x^{2/3}
  75. Optimization 1
  76. Optimization 2
  77. Optimization 3
  78. Optimization - Maximizing Profit
  79. Newton's Method 1
  80. Newton's Method 2
  81. Differentials 1
  82. Differentials 2

Course Description

In this first in a collection of seven series of calculus lessons, Math Doctor Bob (Robert Donley) walks you through the very first steps of differential calculus: Limits; continuity; intermediate value theorem; bisection method; tangent lines; derivatives; optimization; Newton's Method; and differentials.

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