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Active Prelude to Calculus

Preface Features of the Text

Instructors and students alike will find several consistent features in the presentation, including:
Motivating Questions
At the start of each section, we list 2–3 motivating questions that provide motivation for why the following material is of interest to us. One goal of each section is to answer each of the motivating questions.
Preview Activities
Each section of the text begins with a short introduction, followed by a preview activity. This brief reading and preview activity are designed to foreshadow the upcoming ideas in the remainder of the section; both the reading and preview activity are intended to be accessible to students in advance of class, and indeed to be completed by students before the particular section is to be considered in class.
A typical section in the text has at least three activities. These are designed to engage students in an inquiry-based style that encourages them to construct solutions to key examples on their own, working in small groups or individually.
There are dozens of college algebra and trignometry texts with (collectively) tens of thousands of exercises. Rather than repeat standard and routine exercises in this text, we recommend the use of WeBWorK with its access to the Open Problem Library (OPL) and many thousands of relevant problems. In this text, each section includes a small collection of anonymous WeBWorK exercises that offer students immediate feedback without penalty, as well as 3–4 additional challenging exercises per section. Each of the non-WeBWorK exercises has multiple parts, requires the student to connect several key ideas, and expects that the student will do at least a modest amount of writing to answer the questions and explain their findings.
As much as possible, we strive to demonstrate key fundamental ideas visually, and to encourage students to do the same. Throughout the text, we use full-color 7  graphics to exemplify and magnify key ideas, and to use this graphical perspective alongside both numerical and algebraic representations of calculus.
Interactive graphics
Many of the ideas of how functions behave are best understood dynamically; applets offer an often ideal format for investigations and demonstrations. Desmos provides a free and easy-to-use online graphing utility that we occasionally link to and often direct students to use. Thanks to David Austin, there are also select interactive javascript figures within the text itself.
Summary of Key Ideas
Each section concludes with a summary of the key ideas encountered in the preceding section; this summary normally reflects responses to the motivating questions that began the section.
To keep cost low, the graphics in the print-on-demand version are in black and white. When the text itself refers to color in images, one needs to view the .html or .pdf electronically.