2.5 Continuity

By the end of your studying, you should know:
Onscreen applet instructions:
h → 0, i.e. to let x → 1. Note the different effects if you approach from
the right vs. the left.
ExamplesWhat isWhat is Is x continuous at 0?
Consider the function
A hiker sets out at dawn to walk over a mountain and down the other side to a lake, a distance of x kilometers, and he reaches his destination exactly 12 hours later. He camps, then leaves at the same time the next morning and travels the same trail back, arriving at his starting place 12 hours later. Use the Intermediate Value Theorem to show that at some specific time, he was at the same place on his hike on both days. AppletsContinuity of Functions
VideosSee short videos of worked problems for this section.
QuizExercisesSee Exercises for 2.5 Continuity (PDF).Work online to solve the exercises for this section, or for any other section of the textbook. 
Resources on the WebInformation on NewtonBiographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Information on Leibniz
Calculus Applications
Continuity

Interesting Application
Question: Which theorem allows us to conclude that if the balloon has a maximum height of 50 meters and a minimum height of 20 meters as it passes through the valley, then it must have gone through a point 37 meters above the valley floor? Why? 
2.4 Limits at Infinity  Table of Contents  2.6 Tangent Lines and Their Slopes 
Software requirements: For best results viewing and interacting with this page, get the free software listed here.
Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel