AP CALCULUS AB



AP CALCULUS AB

LIMIT WORKSHEET #1

Find the indicated limit. Which method is most appropriate: Direct Substitution, Numerical, Analytic or Graphical?

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

7. [pic]

8. [pic]

9. [pic]

10. [pic]; where [pic]

11. [pic]; where [pic]

Find the discontinuities (if any) for each function. Identify which are Removable and which are Nonremovable Jump or Nonremovable Infinite? Analyze each initially without a graph, then draw a sketch afterwards to confirm.

12. [pic]

13. [pic]

14. [pic]

15. [pic]

16. [pic]

17. [pic]

18. [pic]

19. [pic]

ANSWERS

1. -7

2. 1

3. -5

4. –(

5. (

6. 3x^2

7. 2

8. -1/2

9. 1

10. DNE

11. 3

12. None, contin (-(,()

13. Nonremovable @ x = +/-1

14. Nonremovable @ every integer

15. Removable @ x = 1

16. Removable @ x = -1

AP CALCULUS AB

LIMIT WORKSHEET #2

Find the indicated limit.

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

7. [pic]

8. [pic]

9. [pic]

10. [pic]

11. [pic]

12. [pic]

13. [pic]

14. [pic]

15. [pic]

16. [pic]

Answers:

1. 1

2. 1

3. [pic]

4. [pic]

5. [pic]

6. 0

7. 0

8. [pic]

9. [pic]

10. [pic]

11. 2

12. [pic]

13. 4

14. 1

15. [pic]

16. 0

AP CALCULUS AB

LIMIT WORKSHEET #3

Find the indicated limit.

1. [pic]

2. [pic]

3. [pic]

4. [pic] where [pic]; (Graphically)

5. [pic]

6. [pic]

7. [pic]

8. [pic]

9. [pic]

10. [pic]

11. [pic]

12. [pic]

13. [pic]

14. [pic]

15. [pic]

16. [pic]

17. [pic]

18. [pic]

19. [pic]

20. [pic]

Find the interval for which the function is continuous.

21. [pic]

22. [pic]

23. [pic]

24. [pic]

Find the discontinuities (if any) for the given function. State whether they are Removable, Nonremovable Jump or Nonremovable Infinite. Use your TI-83/84 to verify your responses.

25. [pic]

26. [pic]

27. [pic]

28. [pic]

29. [pic]

30. [pic]

31. [pic]

Answers:

1. 1

2. 0

3. [pic]

4. 1

5. [pic]

6. [pic]

7. [pic]

8. -2

9. 1

10. 2.718 … “e”

11. -3

12. [pic]

13. [pic]

14. 0

15. 2

16. 1

17. [pic]

18. 10x

19. [pic]

20. 0

21. [pic]

22. [pic]

23. [pic]

24. [pic]

25. Continuous for[pic]

26. 1, Removable; -2 Nonremovable Infinite

27. Continuous for[pic]

28. 1, Removable

29. Continuous for[pic]

30. 2, Nonremovable Jump

31. Continuous for[pic]

AP CALCULUS AB

LIMIT WORKSHEET #4

Find each of the following limits.

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

7. [pic]

8. [pic]

9. [pic]

10. [pic]

11. [pic]

12. [pic]

13. [pic]

14. [pic]

15. [pic]

16. [pic]

17. [pic]

18. [pic]

19. [pic]

20. [pic]

21. [pic]

22. [pic]; where [pic]

23. [pic]; where [pic]

Answers:

1. [pic]

2. 0

3. [pic]

4. 0

5. 1

6. 10

7. 4

8. 1

9. 3

10. 1

11. -1

12. 0

13. [pic]

14. [pic]

15. 3

16. 4

17. Does not exist

18. [pic]

19. Does not exist

20. [pic]

21. 0

22. 2

23. Does not exist

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