Wow! Limits are the first step in understanding Calculus and it’s a very simple idea taken to the extreme! We are looking very closely at how functions exist as we get very, Very, VERY close to a specific point. This idea is simple for friendly functions at easy points, but get extremely complex as we talk about unfriendly functions at “interesting” points. I know my language for “unfriendly” and “interesting” are not well defined, however, throughout this unit, you will learn more about these and come to understand what this means.
Meanwhile, let’s understand what will be in this unit of learning:
- EU 1.1 – The concept of a limit can be used to understand the behavior of a function.
- Express limits symbolically an using correct notation.
- Interpret limits expressed symbolically.
- Estimate limits of functions.
- Determine limits of functions.
- Deduce and interpret behavior of functions using limits.
- EU 1.2 – Continuity is a key property of functions that is defined using limits.
- Analyze functions for intervals of continuity or points of discontinuity.
- Determine the applicability of important calculus theorems using continuity.