Evaluating Limits Analytically

1. Evaluating Limits Analytically Today you will use the properties of limits to evaluate limits algebraically. You will also evaluate limits involving infinity algebraically and conceptually.

2. Properties of LimitsWhen limits exist, there is nothing unusual about the way they interact algebraically with each other. You could easily predict that the following properties would hold.

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. Limits at Infinity of Polynomial Functions

7. Limits at Infinity of Polynomial Functions When you are evaluating limits at Infinity of Polynomial Functions, you are really just looking at the “end behavior” of the graph of the polynomial. What happens on the left side (as x approaches negative infinity) of the graph? Does it continue to increase or decrease? Does it approach an asymptote? What happens on the right side (as x approaches positive infinity) of the graph? Does it continue to increase or decrease? Does it approach an asymptote? When you are evaluating limits at infinity for polynomial functions, use your knowledge of their end behavior to help you.

8. Evaluate each limit.

9. Flowchart for Evaluating Limits Analytically

10. Assignment A1.11 Sect II See yu tmrrw!