Basic cal

1. Basic Calculus
Science, Technology, Engineering, and Mathematics
Lesson 2.1
The Basic Limit Laws

2. 2

3. 3
How can we determine the limit
of a function without graphing
the function or using table of
values?

4. Learning Competency
At the end of the lesson, you should be able to do the following:
4
Illustrate the limit laws (STEM-BC11LC-IIIa-3).

5. Learning Objectives
At the end of the lesson, you should be able to do the following:
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∙ Determine the limit of a function without using
table of values or using its graph.
∙ Apply the different limit laws in evaluating limit of
a function.

6. 6
The Basic Limit Laws

7. 7
Limit of a Constant Function

8. 8
Limit of an Identity Function

9. 9
Constant Multiple Law

10. 10
Sum or Difference Law

11. 11
Sum or Difference Law

12. 12
Product Law

13. Remember
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14. 14
Quotient Law

15. 15
Quotient Law

16. 16
Power Law

17. 17
Power Law

18. 18
Root Law

19. 19
Root Law

20. 20

21. Let’s Practice!
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22. Let’s Practice!
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23. Try It!
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24. Tip
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25. Tip
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Note that direct substitution may not
be applicable to some limits that will be
discussed in the next lesson.

26. Let’s Practice!
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27. Let’s Practice!
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28. Try It!
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29. Let’s Practice!
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30. Let’s Practice!
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31. Try It!
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32. Check Your Understanding
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Use the limit laws to evaluate the following limits.

33. Check Your Understanding
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34. Let’s Sum It Up!
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Basic Limit Laws
• Limit of a Constant Function
• Limit of an Identity Function
• Constant Multiple Law
• Sum or Difference Law
• Product Law
• Quotient Law
• Power Law
• Root Law

35. Key Formulas
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Limit Laws Formula
Limit of a Constant Function
Limit of an Identity Function
Constant Multiple Law
Sum or Difference Law

36. Key Formulas
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Limit Laws Formula
Product Law
Quotient Law
Power Law

37. Key Formulas
37
Limit Laws Formula
Root Law

38. Challenge Yourself
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39. Bibliography
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Edwards, C.H., and David E. Penney. Calculus: Early Transcendentals. 7th ed. Upper Saddle River, New
Jersey: Pearson/Prentice Hall, 2008.
Larson, Ron H., and Bruce H. Edwards. Essential Calculus: Early Transcendental Functions. Boston:
Houghton Mifflin, 2008.
Leithold, Louis. The Calculus 7. New York: HarperCollins College Publ., 1997.
Smith, Robert T., and Roland B. Milton. Calculus. New York: McGraw Hill, 2012.
Tan, Soo T. Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach. Australia:
Brooks/Cole Cengage Learning, 2012.