MA101: Single-Variable Calculus I

2.5: Adjectives for Functions

• Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Section 2.5: Adjectives for Functions" URL

  Read Section 2.5 (pages 51-54). The intuitive notion of a continuous function is made precise using limits. In addition, you will be introduced to the Intermediate Value Theorem, which rigorously captures the intuitive behavior of continuous real-valued functions.
  

• 2.5.1: Continuous Functions

  • Temple University: Gerardo Mendoza's and Dan Reich's "Calculus on the Web" URL

    Click the link to Book I, and click on the "Index" button. Click on button 26 (A missing value). Work on problems 15-26. Return to the "Index," and click on button 27 (Discontinuities of simple piecewise defined functions). Complete problems 1-10. If at any time the problem set becomes too easy for you, feel free to move on. 

• 2.5.2: Differentiable Functions

  • Temple University: Gerardo Mendoza's and Dan Reich's "Calculus on the Web" URL

    Click the link to Book I, and click on the "Index" button. Click on button 39 (Differentiability). Complete problems 1-10. If at any time the problem set becomes too easy for you, feel free to move on.

• 2.5.3: The Intermediate Value Theorem

  • PatrickJMT: "Intermediate Value Theorem" Page

    Watch this brief video for an explanation on the Intermediate Value Theorem.