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?"


5. Assignment: 
   	Study for the test on Sections 4.1 – 4.4

       

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