BUS-221 Quantitative Methods LECTURE 8

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.

Topics Review topics -Functions -Algebra -Calculus -Application

Absolute Value (1 of 6)

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

Absolute Value (3 of 6) Example 1 – Continued

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

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

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

Summation Notation (1 of 4)

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

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

Summation Notation (4 of 4) Example – Continued

Sequences (1 of 11)

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

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

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:

Sequences (5 of 11)

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

Sequences (7 of 11)

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

Sequences (9 of 11)

Sequences (10 of 11)

Sequences (11 of 11) Example – Repeating Decimals

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

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

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

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

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

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

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

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

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

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

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

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

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