Limits a Geometric and Numeric ApproachLimits Using Tables
Consider the function
x2 - 1
Notice that this function is undefined at x = -1. In calculus undefined is not as precise as possible. Instead one asks, what does the y value "look like" when the x value is near -1. The table below demonstrates:
If the y value does not tend toward a single number as
x tends towards a,
then we say that the limit does not exist as x approaches
Looking at the graph of a function is another convenient way of determining a limit. For example, a computer was used to graph the the function
x2 - 1
Choose a function and a number. Let partner A select a y range.
Partner B must find an x range so that the graph leaves the box on
the sides and not the top and bottom. If Partner B can always win,
then the function has a limit at that number. We will play this game
first with me as Partner B and the class as Partner A.
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