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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