Business Calculus
 Course Contract
 Quiz 1: January 22
 Note. When opening a math 'html' file in this web
page, it is preferable to use 'Internet Explorer'.
 Review on PreCalculus or College Algebra:

Exponents and Radicals
 page 018:,31,33,35,37,39.

Factoring
 page 024: Odd numbers, 17,1949.
 Practices on factorings
 Exercises on Quadratic Equations.
 More Exercises on Factorings (added on January 12/07).

Rational
Expressions
 page 032: 13,15,17,19.
 Exercise on solving absolute value inequalities.
 More exercises on Linear Inequalities and Absolute Value Inequalities.
 Solving Quadratic Inequalities
 Standard Equation of a circle:
 Line
Equations
 Word Problems: Break Even Analysis, Rental Car Problem and etc.
 Example: You are about to take a trip and you plan to rent a car, here are two rental offers: (i) Hertz will give you 30 cents per mile and $45 per day, and (ii) Avis will give you 25 cents per mile and $50 per day. Suppose you decide to rent a car for 4 days. Which company offers you a better deal? Explain. Answer.
 Example A manufacturer of electronic
components finds that in making x units of a product weekly it has a
cost of $2 per unit, plus a fixed cost of $1800. Each unit sells for $5.
 Find the cost, revenue and profit functions.
 Sketch these functions.
 Find the breakeven point.
 Practice Problems

Functions
 Recall vertical line test, when will the graph represent a function?
 Domain and Range:
(a) When you know the graph of a function, you can tell what the domain (inputs or x) and range (outputs or y) are.  Drills on finding the domain of a function.
 Shifting and Reflection Techniques:
 Horizontal Shifting: y = f(x + a) is a horizontal shifting of y = f(x). If a > 0, then the graph will be shifted to the left; if a <0, then the graph will be shifted to the right.
 Vertical Shifting: y = f(x) + a is a vertical shifting of y = f(x). If a > 0, then the graph will be shifted up; if a <0, then the graph will be shifted down.
 y =  f(x) is a reflection of y = f(x).
 Practices on Shifting, Expansions and etc (CASIO file)
 Tutorial on polynomial functions.
 More on polynomial functions
 Review for an old test 2.
 Extra Credits
 Limits (skip
Maple file)
 Numerical Explorations on Limits. (html file)
 Drill.
 Exercises from pages 5860, #5,9,17,19,21,25,27,31,35,41,43,45.
 Continuous Function (html
file)
 Drill (Do only the first two exercises, skip the trig functions).
 Exercises from pages 6970: #1 through 25 odd; 49, 50.
 Concept of tangent lines. (html)
 Exploration.
 Tangent line at a point and the function (zooming in).
 Derivative Functions:
 (A flash) Derivative at a point a is the slope of the tangent line at the point a.
 How do we find the derivative at one point? (an avi file)
 Drill on the definition.
 Finding the derivative at one point numerically and algebraically. (Maple file)
 NOTES on Understanding the Concepts of Derivatives
 Rules of finding derivatives and etc.
 An old test 3.
 An old practice test 4. [Study this for quiz on March 23.]
 HW for Section 2.4: page 129, #2337 odd numbers.
 Practice for test 3. (Added on April 2, 2007)
 Review for an old test 4.
 Marginal Analysis.
 Investigating max/min and inflection points (Maple file)
 More practices on finding derivatives, horizontal tangents and etc.
 Applications to Product and Quotient Rule.
 Chain Rule and etc
 Maximum, Minimum, First Derivative Test
 Second Derivative
 Sharp Corners and Vertical Tangents.
 (Skip) Help on Word Problems
 (Skip) Rational Functions.
 Second Derivative
 April 11: An old practice test 5 (Do number 3 through 7)
 **April 20: Quiz 4/Test 4 (Due April 23).
 Word Problems.
 Applications:
 Open box problem: An open box is to be made from a 16 in. by 30 in. piece of cardboards by cutting out squares of equal size from the four corners and bending up the sides. What size should the squares be to obtain a box with largest possible volume?
 **Review for the final exam.
 Some animations and graphs related to Mathematics