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Lesson 3: The Limit of a Function

The document provides an introduction to the precise definition of a limit in calculus. It begins with a heuristic definition of a limit using an error-tolerance game between two players. It then presents Cauchy's precise definition, where the limit is defined using epsilon-delta relationships such that for any epsilon tolerance around the proposed limit L, there exists a corresponding delta tolerance around the point a such that the function values are within epsilon of L when the input values are within delta of a. Examples are provided to illustrate the definition. Pathologies where limits may not exist are also discussed.

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Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function
Lesson 3: The Limit of a Function