CALCULUS I
Mrs.Volynskaya AP Calculus Name: ___________________
Worksheet L.1-2
Refer to the graph to find each limit, if it exists:
a. [pic] b. [pic] c. [pic] d. [pic] e. [pic] f. [pic]
1. 2.
a. _____ b. _____ c. _____ a. _____ b. _____ c. _____
d. _____ e. _____ f. _____ d. _____ e. _____ f. _____
3. 4.
a. _____ b. _____ c. _____ a. _____ b. _____ c. _____
d. _____ e. _____ f. _____ d. _____ e. _____ f. _____
5. 6.
a. _____ b. _____ c. _____ a. _____ b. _____ c. _____
d. _____ e. _____ f. _____ d. _____ e. _____ f. _____
7. 8. 9.
a. [pic]= _____ a. [pic]= _____ a. [pic]= _____
b. [pic]= _____ b. [pic]= _____ b. [pic]= _____
c. f(2) = _____ c. [pic]= _____
d. f(1) = _____
10. True or false?
_____ a. [pic]= -1
_____ b. [pic]= 1
_____ c. [pic]= 1
_____ d. [pic]exists
_____ e. [pic]= 1
_____ f. [pic] DNE
_____ g. [pic]= 1
_____ h. [pic]= [pic]
_____ i. [pic]exists
_____ j. [pic]= 1
_____ k. [pic]exists at every c on the interval (-1,1)
_____ l. [pic]exists at every c on the interval (1,3)
Calculus Name: _____________________________
Worksheet L.1-2
Based on the graph evaluate the following.
1. [pic]= _____ 11. [pic]= _____
2. [pic]= _____ 12. [pic]= _____
3. [pic]= _____ 13. [pic]= _____
4. [pic]= _____ 14. f(6) = _____
5. [pic]= _____ 15. [pic]= _____
6. [pic]= _____ 16. f(3) = _____
7. [pic]= _____ 17. [pic]( _____
8. f(1) = _____ 18. f(−1) ( _____
9. f(0) = _____ 19. True or False: [pic]exists at every c on (1,3)
10. f(−2) = _____ 20. True or False: [pic]exists at every c on (−2,1)
Evaluate the following.
21. [pic] = _____ 22. [pic] = _____ 23. [pic] = _____ 24. [pic] = _____
25. [pic] = _____ 26. [pic] = _____
27. [pic] = _____ 28. [pic] = _____
29. [pic] = _____ 30. [pic] = _____
31. [pic] = _____ 32. [pic] = _____
33. [pic] = _____ 34. [pic] = _____
35. [pic] = _____ 36. [pic] = _____
37. [pic] = _____ 38. [pic] = _____
39. [pic] = _____ 40. [pic] = _____
41. [pic] = _____ 42. [pic] = _____
1 – 2x, x ( 1
43. [pic]f(x) =
x – 3, x ( 1
(a graph may help)
x + 2, x ( −1
44. [pic]f(x) =
x2, x ( 1
(a graph may help)
45. Suppose [pic]and [pic]find the [pic]
Calculus Name: _____________________________
Worksheet L.2-1
Find the 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]
Calculus Name: _____________________________
Worksheet L.2-2
Evaluate the following.
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]= 23. [pic]= 24. [pic]=
25. [pic]= 26. [pic]= 27. [pic]=
28. [pic]= 29. [pic]= 30. [pic]=
31. [pic]= 32. [pic]= 33. [pic]=
34. [pic]= 35. [pic]= 36. [pic]=
37. [pic]= 38. [pic]= 39. [pic]=
40. [pic]= 41. [pic]= 42. [pic]=
43. [pic]= 44. [pic] = 45. [pic]=
Calculus Name: _____________________________
Worksheet L.3
Evaluate the following.
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]
Calculus Name: _____________________________
Worksheet L.4-1
Refer to the graph to find each of the following:
a) the value(s) of x for which the function is discontinuous
b) why it is discontinuous at that value
c) the type of discontinuity
d) whether it is removable (R) or nonremovable (NR) discontinuity
1) 2) 3)
a) ______________ a) ______________ a) ______________
b) ______________ b) ______________ b) ______________
c) ______________ c) ______________ c) ______________
d) ______________ d) ______________ d) ______________
4) 5) 6)
a) ______________ a) ______________ a) ______________
b) ______________ b) ______________ b) ______________
c) ______________ c) ______________ c) ______________
d) ______________ d) ______________ d) ______________
Given the following graph, state for what values of x the function is discontinuous and state why it is discontinuous at that point. Also state what type of discontinuity it is and whether it is removable or nonremovable. Explain how any removable discontinuities should be defined or redefined to make the function continuous.
|Where? |Why? |Type |Removable (R) or Nonremovable |If R, what values makes it |
| | | |(NR) |continuous? |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
Find the value of k that makes the function continuous.
[pic]
At what points, if any, is the function f(x) =[pic] discontinuous?
Calculus Name: _____________________________
Worksheet L.4-2
Draw a graph with the following conditions.
Function #1
□ f(0) = 0 ( [pic]
□ f(1) = 2 ( [pic]
□ f(-1) = -2
□ at f(3) there is a non-removable discontinuity
□ at f(-4) there is a removable discontinuity
Function #2
□ [pic] ( [pic]
□ [pic] ( [pic]
□ f(0) = 0
□ at f(-4) there is a removable discontinuity
□ [pic]exists, but the graph is discontinuous
Function #3
□ [pic] ( [pic]
□ [pic] ( [pic]
□ f(0) = 0 ( [pic]
□ [pic]exists, but the graph is discontinuous
Function #4
□ [pic] ( [pic]
□ [pic] ( [pic]
□ f(-1) = 0 ( f(2) = 1
□ [pic] does not exist
Function #5
□ f(-3) = 0 ( f(0) = 3
□ [pic] ( [pic]
□ [pic]
□ at f(5) there is a removable discontinuity
□ [pic] does not exist
Function #6
□ [pic] ( [pic]
□ [pic] ( [pic]
□ f(0) = 1
□ [pic]exists, but the graph is discontinuous
Function #7
□ f(0) = 0 ( [pic]
□ f(2) = 1 ( [pic]
□ f(-2) = -4
□ [pic] does not exist
□ [pic]exists, but the graph is discontinuous
Function #8
□ [pic] ( [pic]
□ [pic] ( [pic]
□ [pic] ( [pic]
□ f(0) = 2
□ at f(-5) there is a non-removable discontinuity
Calculus Name: _____________________________
Limits Practice Test
Refer to the graph to evaluate the following:
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. _______ True or False: [pic] exists for every c in the interval (2,10)
20. _______ True or False: [pic] exists for every c in the interval (−2,2)
Refer to the graph to find the following:
a) the value(s) of x for which the function is discontinuous
b) why it is discontinuous at that value
c) the type of discontinuity
d) whether it is a removable (R) or nonremovable (NR) discontinuity
e) if it is removable, how could you make the function continuous at that point?
| |Where? |Why? |Type? |Removable (R) or Nonremovable (NR)? |If R, what values make it |
| | | | | |continuous? |
|21. | | | | | |
|22. | | | | | |
|23. | | | | | |
|24. | | | | | |
Evaluate the following.
25. _______ [pic] 26. _______ [pic]
27. _______ [pic] 28. _______ [pic]
29. _______ [pic] 30. _______ [pic]
31. _______ [pic] 32. _______ [pic]
33. _______ [pic] 34. _______ [pic]
35. _______ [pic] 36. _______ [pic]
37. _______ [pic] 38. _______ [pic]
39. _______ [pic] 40. _______ [pic]
41. _______ [pic] 42. _______ [pic]
43. _______ [pic] 44. _______ [pic]
45. _______ [pic] 46. _______ [pic]
47. _______ [pic] 48. _______ [pic]
49. _______ [pic] 50. _______ [pic]
51. _______ [pic] 52. _______ [pic]
53. _______ [pic] 54. _______ [pic]
55. _______ [pic] 56. _______ [pic]
57. _______ [pic] 58. _______ [pic]
59. _______ [pic] 60. _______ [pic]
61. _______ [pic] 62. _______ [pic]
63. _______ [pic] 64. _______ [pic]
Find the points of discontinuity. If there are no such points, write “none”.
65. _______ [pic] 66. _______ [pic]
67. _______ [pic] 68. _______ [pic]
69. _______ [pic] 70. _______ [pic]
71. _______ [pic] 72. _______ [pic]
Find the values of a and k that make the function continuous.
[pic] [pic]
73. a = _______ k = _______ 74. a = _______ k = _______
75. Draw a graph with the following conditions:
( [pic]
( [pic]
( [pic]
( [pic]
( at f(−3) the limit exists but the graph is discontinuous
( at f(3) there is a non-removable discontinuity
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- use of calculus in economics
- calculus in economics examples
- prostatic urethral calculus icd 10
- ureteral calculus icd 10
- calculus of ureter icd 10
- list of calculus derivative rules
- calculus derivatives
- calculus 3 chain rule calculator
- calculus derivatives pdf
- calculus derivative rules cheat sheet
- chain rule calculus examples
- calculus tutorial pdf