1. Techniques for Computing Limits: The Limit Laws
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”)

9. -

10. Example 4

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

13. D. Special Trigonometric Limits
Theorems:

14. Examples:

15. The Squeeze Theorem

17. Example (using the Squeeze Theorem):