A Beginning Look at Calculus

Activities

Presentations

Challenge Options

Many of the handouts have embedded challenge options

Outline

— We will start the investigation exploring area under the curve and slope at a point, both major themes of calculus.

— We will review various types of functions such as piecewise-defined, composite, inverse, and even/odd functions. We will describe their graphs, including stating their domain and range. We will explore the behavior of graphs at the far left and right, as well as any holes or asymptotes within the graph.

— We will study slope by examining finite differences. We will learn to write slope statements and sketch slope functions.

— In collaboration with your Physics class, we will use graphs to analyze motion. We will
determine average velocity on distance graphs and velocity graphs. You will discover the relationships among total distance, displacements, velocity, speed, and acceleration.

— We will examine area and slope on distance and velocity graphs to find a relationship
between them
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Goals

• Build a positive team climate for learning calculus.
• Review/master pre-calculus topics.
• Calculate volumes of solids geometrically.
• Investigate finite differences.
• Explore slope.
• Examine the relationship between position and velocity graphs.