1. 1.2 – Algebraic Limits and Continuity

2. Find the following limits using the Limit Properties: 1.2 – Algebraic Limits and Continuity

3. Find the requested limits for the given function. 1.2 – Algebraic Limits and Continuity Theorem on Limits of Rational Functions

4. Find the following limits: 1.2 – Algebraic Limits and Continuity

5. Find the following limits: 1.2 – Algebraic Limits and Continuity

6. Find the following limits: 1.2 – Algebraic Limits and Continuity

7. A continuous function is one that can be plotted without the plot being broken. Is the graph of f(x) a continuous function on the interval [0, 4]? No At what values of x is the function discontinuous and why? Yes 1.2 – Algebraic Limits and Continuity

8. What are the rules for continuity at a point? 1.2 – Algebraic Limits and Continuity

12. 2012 Pearson Education, Inc. All rights reserved Is the following function continuous at x = 3?

13. 1.2 – Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Is the following function continuous at x = –2?

14. 1.3 – Average Rates of Change The average rate of change of y with respect to x, as x changes from x 1 to x 2, is the ratio of the change in output to the change in input: Definition: where x 2 ≠ x 1. Examining the graph of the function, the average rate of change and the slope of the line from P(x 1, y 1 ) to Q(x 2, y 2 ) are the same. The line through P and Q, is called a secant line.

15. 1.3 – Average Rates of Change

16. Average Rate of Change or Slope of the Secant Line     Secant line

17. 1.3 – Average Rates of Change Average Rate of Change or Slope of the Secant Line     Secant line

18. 1.3 – Average Rates of Change Average Rate of Change or Slope of the Secant Line The Difference Quotient Find the simplified difference quotient and the values of the difference quotient for the given values of x and h.

19. 1.3 – Average Rates of Change

20. Average Rate of Change or Slope of the Secant Line The Difference Quotient Find the simplified difference quotient and the values of the difference quotient for the given values of x and h.

21. 1.3 – Average Rates of Change

22. 210 miles were traveled from 2 to 5 hours.

23. 1.3 – Average Rates of Change