1.3: Continuity as a Property of Functions
Some functions are continuous, while others are not, which is evident when looking at a graph of a function. Discontinuity can occur when there are rational functions, and examples are cost of a product and medical interactions. The speed of an automobile during heavy traffic is where one can see continuity in action because at times you are moving at a constant speed and at other times the car has stopped.
Subunit 1.3 explores the continuity as a property of functions. Continuity is evident in various calculus theorems as well as in one-sided limits. This concept will be applied when looking at functions within unit 2.
Read this section on finding limits. Watch the videos in the section as well. This reading discusses how to understand continuous function properties, one-sided limits, and solving problems using the min-max and intermediate value theorem. Then, complete review questions 7-10 toward the bottom of the page. These exercises will provide you with the opportunity to solve problems using the max-min and intermediate value theorems. The solutions to these problems are located here.
Complete exercises 3-6 and 37-39. These exercises will provide you with the opportunity to find one-sided limits. The solution for each problem can be found by clicking on the gray triangle beside each problem. The solution includes detailed work on how to find the given limit.