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The Formal Definition of Limit

The Formal Definition of Limit. Let f be a function defined on an open interval containing c (except possibly at c), And let L be a real number. The statement means that for each there exists a such that if then .

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The Formal Definition of Limit

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  1. The Formal DefinitionofLimit

  2. Let f be a function defined on an open interval containing c (except possibly at c), And let L be a real number. The statement means that for each there exists a such that if then

  3. There are basically 2 kinds of problems you can expect using the formal definition of limit: 1) Given epsilon, find delta (Or, given delta, find epsilon) 2) Limit proofs using the epsilon-delta definition of limit.

  4. Example: Given the limit Find such that whenever

  5. There are 2 steps to an epsilon-delta proof of a limit: Relate the gap to Choose in terms of

  6. Let . Show that

  7. Use the limit definition to prove that

  8. Homework: page 122 # 1, 3, 5, 10, 13, 15, 19 Use your calculator on #10

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