1. Evaluating Limits Analytically
Lesson 2.3

2. What Is the Squeeze Theorem?
Today we look at various properties of limits, including the Squeeze Theorem

3. Basic Properties and Rules
Constant rule
Limit of x rule
Scalar multiple rule
Sum rule (the limit of a sum is the sum of the limits)
See other properties pg

4. What stipulation must be made concerning D(x)?
Limits of Functions
Limit of a polynomial P(x)
Can be demonstrated using the basic properties and rules
Similarly, note the limit of a rational function
What stipulation must be made concerning D(x)?

5. Try It Out
Evaluate the limits
Justify steps using properties

6. General Strategies

7. Some Examples Consider Strategy: simplify the algebraic fraction
Why is this difficult?
Strategy: simplify the algebraic fraction

8. Reinforce Your Conclusion
Graph the Function
Trace value close to specified point
Use a table to evaluate close to the point in question

9. Some Examples
Rationalize the numerator of rational expression with radicals
Note possibilities for piecewise defined functions

10. Three Special Limits
Try it out!
View Graph
View Graph
View Graph

11. Squeeze Rule
Given g(x) ≤ f(x) ≤ h(x) on an open interval containing c And …
Then

12. Assignment Lesson 2.3A Page 87 Exercises 1-43 odd Lesson 2.3B Page 88
Exercises 45 – 97 EOO