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 |