AP Calculus Lesson 1.1: Limits (An Intuitive Approach)

The concept of a limit is the fundamental building block on which all calculus concepts are based. In this lesson we will study limits informally, with the goal of developing an intuitive feel for the basic ideas. In the next lessons we will focus on computational methods and precise definitions.

Many of the ideas of calculus originated with the following two geometric problems:

The Tangent Line Problem:

The Area Problem:

Traditionally, that portion of calculus arising from the tangent line problem is called differential calculus and that arising from the area problem is called integral calculus however, we will see later that the tangent line and area problems are so closely related that the distinction between differential and integral calculus is somewhat artificial.