STAGE  2:  MAPPING  THE  ROUTE

In Stage 1 we assembled and tested our gear. Fully equipped, we are now camped at the base of the mountain named Differential Calculus. A look upward and ahead will reveal many new and interesting ideas, including the derivative and continuity of functions. These will become old friends. Before tackling these ideas, however, we must investigate a fundamental idea that supports all that lies ahead.

The idea that first separates calculus from other areas of mathematics is the concept of a limit. In Stage 2: Mapping the Route, we will look at limits from a distance, just as a mountain climber would try to assess the features of a mountain upon reaching the tree line. We begin with the notions of distance between numbers, approximation, and error tolerance. We introduce the concept of a difference quotient in order to discuss average rates of change.

Objectives

• Distinguish between exact and approximate values.
  • Calculate distances between numbers.
  • Approximate values to within selected error tolerances.
• Compute average rates of change using difference quotients.

LESSON	What To Do: Go to the Onward and Upward area for a description of the graded activities that you must complete in this Stage. There are no graded activities in the Lesson or Practice areas. You will need to complete these graded activities before moving on to the next Stage. Stage 2 Quiz You should go to the Onward and Upward area to plan your week's work in CalculusQuestTM: Stage 2. The Lesson and Practice material will help you prepare for the Stage 2 Quiz.
PRACTICE
ONWARD and UPWARD

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