Lesson #54
Review for Test
Quote of the Day:
"The moving power of mathematical invention is not
reasoning but imagination." -- Augustus de Morgan
Objectives:
The student will review all the concepts of logarithms and
exponential functions.
The student will review the derivatives of logs and
exponential functions.
1. Collect homework.
2. Discuss outline of test:
1-13 Multiple Choice
Find inverse function of y=tan(x), y=ln(x), y=e^x,
y = x/(x+1), etc.
Evaluate logarithmic expressions
Simplify e^(ln(x)+5ln(w))
Solve logarithmic equations
Take derivatives of ln(u), e^u
Take derivatives implicitly
Take derivative of a variable to a variable
Know three definitions of e
14-25 Free Response
Properties of logs
Implicit Differentiation
Prove derivative formula for logs or exponentials
Graph logarithmic or exponential functions
Solve exponential equations
Related Rates Problems
Evaluate logs
Take derivatives of logs and exponentials
(to bases other than e as well as e)
3. Game for review
4. Story about Derivation
The functions are sitting in a bar, chatting
(how fast they go to zero at infinity etc.).
Suddenly, one cries "Beware! Derivation is coming!"
All immediately hide themselves under the tables,
only the exponential sits calmly on the chair.
The derivation comes in, sees a function and says
"Hey, you don't fear me?"
"No, I am e to x", says the exponential self-confidently.
"Well" replies the derivation "but who says I differentiate
along x?"