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”
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:
Polynomial Function
Rational Function with c in its domain
Radical Function with c in its domain
Trigonometric Function with c in its domain

6. Examples

7. Methods for Computing Limits
B. Rational Functions without c in their domain (“Single Holes”)

10. Example 4

11. C. Functions with Radicals

13. D. Special Trigonometric Limits
Theorems:

14. Examples of use:

15. The Squeeze Theorem

17. Example using the Squeeze Theorem: (Watch Video)
Proof of by the squeeze theorem:

18. Another example using the Squeeze Theorem: