CliffsAP Calculus AB and BC
Chapter One
Limits and Continuity
The single major concept that separates precalculus math from calculus is that of the limit
of a function. Although none of the formal definitions of limits are on the AP exam, you must
have a solid, intuitive understanding of how a limit works in order to be able to apply limits to
concepts such as continuity. You must also master a variety of different techniques used to find
limits, because the AP exam will include multiple-choice questions that deal directly with
finding limits.
Intuitive Definition of a Limit
Perhaps the simplest way to understand the concept of the limit of a function is through a
graphical interpretation and in terms of the following translation from calculus to
English:
Calculus <-> English
lim (2x- 1)=? <-> Read: "What is the limit of 2x - 1 as x approaches 2?"
Think: As the x-coordinates get closer and closer to 2 what
values (if any) are the y-coordinates getting closer to?
From the graph, it should be clear that as the x-coordinates get closer and closer to 2, the
y-coordinates get closer and closer ... read full excerpt from CliffsAP Calculus AB and BC, 3rd Edition ebook
