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 Pre-Calculus or College Algebra:
-
Exponents and Radicals
- page 0-18:,31,33,35,37,39.
-
Factoring
- page 0-24: Odd numbers, 1-7,19-49.
- Practices on factorings
- Exercises on Quadratic Equations.
- More Exercises on Factorings (added on January 12/07).
-
Rational
Expressions
- page 0-32: 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 break-even 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 58-60, #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 69-70: #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, #23-37 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