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12. Limits and Derivatives

Section outline

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  Intuitive Idea of Derivatives
  
  Select activity Derivative as a Concept
  
  Derivative as a Concept Lesson
  
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  Limits
  
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  Part 1 Lesson
  
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  Select activity Part 2
  
  
  
  Part 2 Lesson
  
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  Select activity Limit of x^n - a^n / (x - a)
  
  
  
  Limit of x^n - a^n / (x - a) Lesson
  
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  Select activity Limits by Direct Substitution
  
  
  
  Limits by Direct Substitution Lesson
  
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  Select activity Limits by Factoring
  
  
  
  Limits by Factoring Lesson
  
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  Select activity Limits from Tables
  
  
  
  Limits from Tables Lesson
  
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  Limit of Trigonometric Functions
  
  Select activity Limit of Trigonometric Functions
  
  Limit of Trigonometric Functions Lesson
  
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  Select activity Sandwich Theorem
  
  Sandwich Theorem Lesson
  
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  Solved Examples: Exercise 12(a)
  
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  Example 1 Lesson
  
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  Example 2 Lesson
  
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  Example 3 Lesson
  
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  Example 4 Lesson
  
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  Example 5 Lesson
  
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  Example 6 Lesson
  
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  Example 7 Lesson
  
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  Example 8 Lesson
  
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  Example 9 Lesson
  
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  Select activity Example 10
  
  
  
  Example 10 Lesson
  
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  Select activity Example 11
  
  
  
  Example 11 Lesson
  
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  Derivatives
  
  Select activity Introduction
  
  
  
  Introduction Lesson
  
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  Select activity Formal Definition of the Derivative as a Limit
  
  
  
  Formal Definition of the Derivative as a Limit Lesson
  
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  Select activity Worked Example: Derivative from Limit Expression
  
  
  
  Worked Example: Derivative from Limit Expression Lesson
  
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  Select activity Proof of the Constant Derivative Rule
  
  
  
  Proof of the Constant Derivative Rule Lesson
  
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  Select activity Basic Derivative Rules
  
  
  
  Basic Derivative Rules Lesson
  
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  Select activity Basic Derivative Rules: Find the Error
  
  
  
  Basic Derivative Rules: Find the Error Lesson
  
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  Select activity Power Rule
  
  
  
  Power Rule Lesson
  
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  Solved Examples: Exercise 12(b)
  
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  Example 1 Lesson
  
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  Example 2 Lesson
  
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  Solved Examples: Exercise 12( c )
  
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  Example 1 Lesson
  
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  Example 3 Lesson
  
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  Example 4 Lesson
  
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  Example 5 Lesson
  
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  Example 6 Lesson
  
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  Example 7 Lesson
  
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  Example 8 Lesson
  
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  Example 9 Lesson
  
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  Example 10 Lesson
  
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  Example 11 Lesson
  
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  Example 12 Lesson
  
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  Example 13 Lesson
  
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  Example 14 Lesson
  
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  Example 15 Lesson
  
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  Example 16 Lesson
  
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  Example 17 Lesson
  
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  Example 18 Lesson
  
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