Chapter 2(limits)
7
Click here to load reader
-
Upload
eko-wijayanto -
Category
Education
-
view
1.557 -
download
0
description
for engineering math 1
Transcript of Chapter 2(limits)
BMM 104: ENGINEERING MATHEMATICS I Page 1 of 6
CHAPTER 2: LIMITS
Calculating Limits Using the Limit Laws
THEOREM Limit Laws
If L, M, c and k are real numbers and
and then
1. Sum Rule:
2. Difference Rule:
3. Product Rule:
4. Constant Multiple Rule:
5. Quotient Rule:
6. Power Rule: If r and s are integers with no common factor and , then
Example: Attend lecture.
PROBLEM SET: CHAPTER 2
Find the following limits.
1. 19.
2. 20.
3. 21.
4. 22.
5. 23.
6. 24.
7. 25.
BMM 104: ENGINEERING MATHEMATICS I Page 2 of 6
8. 26.
9. 27.
10. 28.
11. 29.
12. 30.
13. 31.
14. 32.
15. 33.
16. 34.
17. 35.
18. 36.
ANSWERS FOR PROBLEM SET: CHAPTER 2
Find the following limits.
1. - 9 19. 1/102. - 26 20. - 1/23. 4 21. - 74. - 16 22. - 35. - 8 23. 3/26. 2/3 24. - 1/37. 5/8 25. - 1/28. - 2 26. - 1/29. 5/2 27. 4/310. 1/5 28. 3/811. 27 29. 1/612. 1 30. 1613. 16 31. 414. - 2 32. - 1/315. 3/2 33. 1/2
BMM 104: ENGINEERING MATHEMATICS I Page 3 of 6
16. 5/4 34. - 3/217. 3/2 35. 3/218. 5/4 36. 5/4
One-Sided Limits and Limits at Infinity
THEOREM
A function f(x) has a limit as x approaches c if and only if it has left-hand and right-hand limits there and these one-sided limits are equal:
and .
THEOREM Limit Laws as
If L, M, and k are real numbers and
and then
1. Sum Rule:
2. Difference Rule:
3. Product Rule:
4. Constant Multiple Rule:
5. Quotient Rule:
6. Power Rule: If r and s are integers with no common factor and , then
Example: Attend lecture.
PROBLEM SET: CHAPTER 2
Finding One-Sided Limits Algebraically
BMM 104: ENGINEERING MATHEMATICS I Page 4 of 6
Find the following limits.
1.
2.
3.
4.
5.
6.
7. a. b.
8. a. b.
Using
Find the following limits.
1. 9.
2. 10.
3. 11.
4. 12.
5. 13.
6. 14.
7. 15.
8. 16.
BMM 104: ENGINEERING MATHEMATICS I Page 5 of 6
Limits of Rational Functions
In the following questions, find the limit of each rational function (a) as and (b) as.
1. 6.
2. 7.
3. 8.
4. 9.
5. 10.
Limits with Noninteger or Negative Powers
Find the following limits.
1. 4.
2. 5.
3. 6.
ANSWERS FOR PROBLEM SET: CHAPTER 2
Finding One-Sided Limits Algebraically
1. 4. 1
2. 0 5.
BMM 104: ENGINEERING MATHEMATICS I Page 6 of 6
3. 1 6.
7. a. 1 b. -18. a. b.
Using
1. 1 9. 22. k 10. 03. ¾ 11. 14. 1/3 12. 15. 2 13. 1/26. 2 14. 5/47. ½ 15. 3/88. 3 16. 12/5
Limits of Rational Functions
1. (a) 2/5 (b) 2/52. (a) 2 (b) 23. (a) 0 (b) 04. (a) 0 (b) 05. (a) 7 (b) 76. (a) 0 (b) 07. (a) 0 (b) 08. (a) 9/2 (b) 9/29. (a) -2/3 (b) -2/310. (a) - 1 (b) - 1
Limits with Noninteger or Negative Powers
1. 0 4.2. - 1 5.3. 1 6. - 5/2
