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Analytical Evaluation and Strategies for Finding Limits in Calculus

Learn how to evaluate limits analytically using properties and techniques such as dividing out and rationalizing. Understand basic limits and properties including scalar multiples, sums, products, quotients, powers, and composite functions. Practice with examples and exercises to master limit evaluation in calculus.

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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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