1. DO NOW: Find

2. HW: Finish WKSH 2.1 and a half – Calculating Limits Using the Limit Laws

3. Example 1

5. Example 2 (a) (b)

6. Direct Substitution If f is a polynomial or a rational function and a is in the domain of f, then Functions with the Direct Substitution Property are called continuous at a Remember: not all limits can be evaluated by direct substitution!

7. Example 3

8. In general, If f(x) = g(x) when x ≠ a, then

9. Example 4

10. Additional Properties of Limits THEOREM If f(x) ≤ g(x) when x is near a (except possibly at a) and the limits of f and g both exist as x approaches a, then

11. The Sandwich Theorem (AKA the Squeeze Theorem) If f(x) ≤ g(x) ≤ h(x) when x is near a (except possibly at a) and then

12. Example 5 Show that

13. Example 5 (Solution)