1. L IMITS AND L IMITS AT INFINITY Limit Review 1

2. Limits can be calculated 3 ways Numerically Graphically Analytically (direct substitution) Properties of limits (pages 56-58)

3. Graphically Determine the value of y as x approaches some number c

4. Formal Definition of a Limit

5. Analytic techniques Direct substitution Factoring- cancel common factors Rationalize- multiply by the conjugate

6. 1)Find 2) Find

7. 3) Find

8. One sided limits left Right Limit existence

9. 4) Find

10. 5) Find

11. Infinite Limits Limit of f(x) increases or decreases without bound as x approaches some number c Limit does not exist DNE Vertical asymptotes occur when limits are infinite Limit as x approaches 1

12. 6) Find

13. 7) Find

14. 8) Find

15. 9) Find

16. Limits at Infinity Identifies the behavior of the function as x tends to infinity If, then L is a horizontal asymptote Usually f(x) is rational Limit as x approaches infinity

17. 10) Find

18. 11) Find

19. Limits at Infinity Shortcuts If the degree is higher in the denominator, then the limit is equal to zero If the degree is higher in the numerator then the limit does not exist If the degrees are the same, then the limit equals the ratio of the coefficients BOBO BOTN EATS DC

20. 12) Find 13) Find

21. 14) Find and all asymptotes

22. 15) Findand all asymptotes

23. H OME W ORK Limits Practice worksheet