Chapter 2  Limits and Continuity"In this chapter, we show how to define and calculate limits of function values. The calculation rules are straightforward, and most of the limits we need can be found by substitution, graphical investigation, numerical approximation, algebra, or some combination of these."
"One of the uses of limits lies in building a careful definition of continuity. Continuous functions arise frequently in scientific work because they model such an enormous range of natural behavior and because they have special mathematical properties." (Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel Kennedy. "Chapter 2." Calculus: Graphical, Numerical, Algebraic. 5th ed. N.p.: Pearson Education, n.d. 59. Print. AP Edition.) 
Chapter 2 reallife math connection.

Lesson 2.1  Rates of Change and Limits
This lesson will teach students to interpret, estimate, and determine limits of function values. Lesson 2.2  Limits Involving Infinity
This lesson will teach students to interpret, estimate, and determine infinite limits and limits at infinity. 
Lesson 2.3  Continuity
This lesson will teach students to analyze functions to find intervals of continuity and points of discontinuity and to determine the applicability of the Intermediate Value Theorem. Lesson 2.4  Rates of Change, Tangent Lines, and Sensitivity
This lesson will teach students to use limits to determine instantaneous rates of change, slopes of tangent lines, and sensitivity to change. 