1. BUS-221 Quantitative Methods
LECTURE 8

2. Learning Outcome
Knowledge - Be familiar with basic mathematical techniques including: linear programming, systems of linear equations, calculus (differential and integral
Communication - Present analyses of business situations from a quantitative point of view. The analysis will demonstrate clarity of expression, use of terminology, knowledge of format, aptness for the user group
Contribution - Plan and manage their learning to ensure adherence to agreed submission dates and class discussion. Prepares homework assignments for in-class discussion.

3. Topics
Review topics
-Functions
-Algebra
-Calculus
-Application

4. Absolute Value (1 of 6)

5. Absolute Value (2 of 6)
Example 1 – Solving Absolute-Value Equations

6. Absolute Value (3 of 6)
Example 1 – Continued

7. Absolute Value (4 of 6) Absolute-Value Inequalities
A summary of the solutions to absolute-value inequalities is given below:
Table 1.1
Inequality (d > 0)
Solution
|x| < d
−d < x < d
|x| ≤ d
−d ≤ x ≤ d
|x| > d
x < −d or x > d
|x| ≥ d
x ≤ −d or x ≥ d

8. Absolute Value (5 of 6)
Example – Solving Absolute-Value Equations

9. Absolute Value (6 of 6)
Example – Properties of Absolute Value

10. Summation Notation (1 of 4)

11. Summation Notation (2 of 4)
Example 1 – Evaluating Sums

12. Summation Notation (3 of 4)
Example 3 – Applying the Properties of Summation Notation

13. Summation Notation (4 of 4)
Example – Continued

14. Sequences (1 of 11)

15. Sequences (2 of 11)
Example 1 – Listing the Terms in a Sequence

16. Sequences (3 of 11)
Example 2 – Giving a Formula for a Sequence

17. Sequences (4 of 11)
A sequence whose rule is defined in terms of itself evaluated at smaller values, and some explicitly given small values, is said to be recursively defined.
An example is the Fibonacci sequence:

18. Sequences (5 of 11)

19. Sequences (6 of 11)
Example – Listing an Arithmetic Sequence

20. Sequences (7 of 11)

21. Sequences (8 of 11)
Example – Listing a Geometric Sequence

22. Sequences (9 of 11)

23. Sequences (10 of 11)

24. Sequences (11 of 11)
Example – Repeating Decimals

25. The Product Rule and the Quotient Rule (1 of 8)
COMBINING RULE 3 The Product Rule:
COMBINING RULE 4 The Quotient Rule:

26. The Product Rule and the Quotient Rule (2 of 8)
Example 1 – Applying the Product Rule

27. The Product Rule and the Quotient Rule (3 of 8)
Example – Differentiating a Product of Three Factors

28. The Product Rule and the Quotient Rule (4 of 8)
Example – Applying the Quotient Rule

29. The Product Rule and the Quotient Rule (5 of 8)
Example – Differentiating Quotients without Using the Quotient Rule

30. The Product Rule and the Quotient Rule (6 of 8)
Example – Continued

31. The Product Rule and the Quotient Rule (7 of 8)

32. The Product Rule and the Quotient Rule (8 of 8)
Example – Finding Marginal Propensities to Consume and to Save

33. The Chain Rule (1 of 5) COMBINING RULE 5 The Chain Rule:
Example 1 – Using the Chain Rule

34. The Chain Rule (2 of 5)
Example 1 – Continued

35. The Chain Rule (3 of 5)
Example – Using the Power Rule

36. The Chain Rule (4 of 5)
Example – Using the Power Rule

37. The Chain Rule (5 of 5)
Example – Differentiating a Product of Powers