Math 205 JW Lecture 6 - Algebra with exponentials and logs; Average Rate of Change; Intro to Limits

Welcome to lecture 6 of Math 205 JW - Elements of Calculus.

In tonight's lecture, we finish our discussion on logs by solving equations involving logarithms and exponentials. We then talk about the graphs of logarithms and how we could figure them out by noting that logs are the inverses of exponentials. We also discover the convenient truth that in solving equations, we can use logs to get rid of exponentials and exponentials to get rid of logs.

We then move on to chapter 2 of our text--the official start of calculus. We start slowly with talking about the average rate of change, and what would you know, the difference quotient as well as the interpretation of slope as rate of change comes in handy here.

We then move on to talking about limits. We define them and play around with the concepts a bit by looking at a few examples. We also introduce the notion of one sided limits, and then run out of time. We will pick up with our discussion of limits in the next class.