1. Evaluating Limits Algebraically AP Calculus Ms. Olifer
Objective:
You will use the properties of limits to evaluate limits algebraically.
You will also evaluate limits involving infinity algebraically and conceptually.

2. Properties of Limits

3. Continuous Intervals
Such functions are “well-behaved” functions on these intervals and their limits can be evaluated by direct substitution.
*Note: All polynomial functions are “well-behaved” functions and therefore are continuous on the interval

4. Limits of a Constant Value: (think about the graph)
Evaluate each limit:
These are continuous functions, so the direction that we are approaching doesn’t necessarily matter.

5. Limits of Polynomial Functions

6. Example

7. Indeterminate Form
We say that f(x) has an indeterminate form (or is indeterminate) at x = c if the formula for f(c) yields an undefined expression of the type

8. WHAT to DO???
STRATEGY:
Transform f(x) algebraically, if possible, into a new expression that is defined and continuous at x = c, and then evaluate the limit by substitution.

9. Flowchart for Evaluating Limits Analytically

10. Example (continued)

12. Multiplying by the Conjugate

13. Evaluate:

15. Infinite But Not Indeterminate
Evaluate:
Substitution leads to
f(x) is not indeterminate at x = 2
Graph on pg. 93
Limit doesn’t exist

16. See yu tmrrw!