Make a list of all definitions in the section (a few words each is fine). Summarize any lengthy definitions introduced in this section in your own words.
- tangent - from the latin, tangens (touching). The tangent line is a line that just touches a curve at a point.
- secant line - a line passing through two points along the arc of a curve.
-
limit notation - in this section, the notation
means that point Q of the graph will tend toward P of the graph, and as it does the slope
will tend toward a value which represents the slope of the
tangent line to the curve at point P. -
Galileo's law - a law of a falling body which we will encounter often in this
course, represented here as
This says that the distance that the body falls grows quadratically.
-
average velocity - calculated as the ratio
- instantaneous velocity - the limit of the average velocity as the time elapsed tends to zero.
Make a list of all theorems (lemmas, corollaries) in the section (a few words each is fine). Summarize each one introduced in this section in your own words.
There were no theorems in this section.
Make a note of any especially useful properties, tricks, hints, or other materials.
Nothing that I noticed.
Summarize the section in two or three sentences.
Here we focus on the concept of the tangent line, and see how it is either approximated or calculated exactly as a limit of a series of secant lines. The slope of the line may have a physical meaning, such as an average or instantaneous velocity.