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Analytical Evaluation and Strategies for Finding Limits in Calculus

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  1. 1.3 Evaluating Limits Analytically

  2. Objectives • Evaluate a limit using properties of limits. • Develop and use a strategy for finding limits. • Evaluate a limit using dividing out and rationalizing techniques.

  3. Basic Limits • Sometimes you can directly substitute.

  4. Examples

  5. Properties of Limits If • Scalar multiple:

  6. Properties of Limits (continued) If • Sum/difference:

  7. Properties of Limits (continued) If • Product:

  8. Properties of Limits (continued) If • Quotient:

  9. Properties of Limits (continued) If • Power:

  10. Example

  11. Example

  12. Composite Function If

  13. Example

  14. Trig Functions

  15. Examples

  16. Another Method • Some limits can’t be solved by direct substitution. When you substitute, you get 0/0.

  17. Example Learn how to factor a cube!

  18. Example

  19. Example

  20. Homework 1.3 (page 65) #1-61 odd

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