1. 15.1 Notes Analytical approach to evaluating limits of rational functions as x approaches a finite number

2. 15.1 Notes Procedure for evaluating limits of rational functions where x approaches a number. 1.Attempt to evaluate the function at the value that x is approaching.

3. 15.1 Notes – Example 1 Procedure for evaluating limits of rational functions where x approaches a number. 1.Attempt to evaluate the function at the value that x is approaching.

4. 15.1 Notes – Example 2 Procedure for evaluating limits of rational functions where x approaches a number. 1.Attempt to evaluate the function at the value that x is approaching. This is called the indeterminate form.

5. 15.1 Notes Procedure for evaluating limits of rational functions where x approaches a number. 1.Attempt to evaluate the function at the value that x is approaching. 2.If step #1 yields division by zero or the indeterminate form, attempt to factor the numerator and denominator and cancel common factors. Then evaluate the resulting function at the value x is approaching.

6. 15.1 Notes – Example 2

7. 15.1 Notes – Example 3

9. 15.1 Notes – Example 4

11. 15.1 Notes Procedure for evaluating limits of rational functions where x approaches a number. 1.Attempt to evaluate the function at the value that x is approaching. 2.If step #1 yields division by zero or the indeterminate form, attempt to factor the numerator and denominator and cancel common factors. Then evaluate the resulting function at the value x is approaching. 3.If step #2 still yields division by zero or the indeterminate form, or the function doesn’t factor, or it factors but there aren’t any common factors, then the limit probably doesn’t exist. Show that the left-hand and right-hand limits approach infinity or negative infinity.

12. 15.1 Notes – Example 4

13. 15.1 Notes – Example 5

16. 15.1 Notes Procedure for evaluating limits of rational functions where x approaches a number. 1.Attempt to evaluate the function at the value that x is approaching. 2.If step #1 yields division by zero or the indeterminate form, attempt to factor the numerator and denominator and cancel common factors. Then evaluate the resulting function at the value x is approaching. 3.If step #2 still yields division by zero or the indeterminate form, or the function doesn’t factor, or it factors but there aren’t any common factors, then the limit probably doesn’t exist. Show that the left-hand and right-hand limits approach infinity or negative infinity.

17. 15.1 Notes – Practice Problems Evaluate the limit. 1. 2. 3.

18. 15.1 Notes – Practice 1

20. 15.1 Notes – Practice 2

21. 15.1 Notes – Practice 3