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1.6. Techniques for Computing Limits: The Limit Laws. Computing Limits. Basic Limits : For real numbers b and c, and positive integers n:. Properties of Limits. Properties of Limits (continued). Methods for Computing Limits. A. “Plug-Ins” (Direct substitution)

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1.6

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  1. 1.6 Techniques for Computing Limits: The Limit Laws

  2. Computing Limits Basic Limits: For real numbers b and c, and positive integers n:

  3. Properties of Limits

  4. Properties of Limits (continued)

  5. Methods for Computing Limits • A. “Plug-Ins” (Direct substitution) • Using these basic limits and properties of limits, we can prove that the limit at c of the following kinds of functions can be evaluated by direct substitution of c for x. • Direct substitution will work for: • Polynomial Functions • Rational Functions with c in domain • Radical Functions with c in domain • Trigonometric Functions with c in its domain

  6. Examples

  7. Methods for Computing Limits B. Rational Functions with c not in domain(“Single Holes”)

  8. -

  9. Example 4

  10. C. Functions with radicals, c not in domain:

  11. D. Special Trigonometric Limits Theorems:

  12. Examples:

  13. The Squeeze Theorem

  14. Example (using the Squeeze Theorem):

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