Chapter 1: Limits
Section 1.2: Precise Definition of a Limit
Example 1.2.2
Use the EpsilonDelta maplet to show that limx→3(3⁢x−4)≠2.
Solution
Start the EpsilonDelta maplet and bring it to the state shown in Figure 1.2.2(a) by the following steps.
In the top row of the interface, enter the function as 3*x - 4, and enter a=3, and L=2 in the appropriate windows.
Set the plot ranges to xmin=0, xmax=5, ymin=0, and ymax=10.
Set ϵ=0.75 and δ=0.40.
Click on the Plot button at the bottom of the Maplet window.
Figure 1.2.2(a) EpsilonDelta maplet and limx→33⁢x−4≠2
Continue exploring the relationship between ϵ and δ.
For the given value of ϵ, can a value of δ be found that satisfies the conditions of Definition 1.2.1?
If one value of ϵ>0 is found for which the conditions of Definition 1.2.1 are not satisfied, then the value of L is shown to be incorrect. The limit either has a different value or does not exist.
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