Calculus I

CHAPTER7

Continuity

In This Chapter

• What it means to be continuous
• Classifying discontinuity
• When discontinuity is removable
• The Intermediate Value Theorem

Now that you understand and can evaluate limits, it’s time to move forward with that knowledge. Flip through any calculus textbook and read some of the most important calculus theorems, and you’ll find that nearly every one contains a significant condition: continuity. In fact, almost none of our most important calculus conclusions (including the Fundamental Theorem of Calculus, which sounds pretty darn important) work if the functions in question are not continuous.

Testing for continuity ...