Math 205 Lecture 7 - Infinite Limits, Limits at Infinity and The Derivative

Welcome to lecture 7 of Math 205 - Elements of Calculus.

In this lecture, we start out going over some new limits territory. We talk about limits at infinity and infinite limits. We look at the relationships between functions to help us compute such limits and also look at limits at infinity of various types of rational functions. These kinds of limits will be important for later, in topics such as curve sketching.

We then move on to the topic we've all been waiting for--tan tan taaaan--Derivatives!

We look at the problem derivatives were meant to solve, and then develop it from the ground up to obtain the limit definition of the derivative. We use this definition to find the derivative of a function and to find its tangent line at a certain point. We end by going over some homework problems, and we will pick up with more on derivatives next class.