Eventually the calculator reaches a value on the x axis which is large enough that it rounds off to a smaller
number than 1.00000000003, which is 1.00000000002. This produces the sudden drop in the graph as
the plot changes from a section of a 1.00000000003
X
graph to a section of a 1.00000000002
X
graph
(which has a shallower gradient).
This section is maintained until the next drop, and so on. Finally, at the value x =
210
11
the inverted value is ×
so small that 1+
1
/
X
becomes exactly 1 and the graph becomes horizontal. Of course this is completely the
wrong value!
Although this explanation may be beyond the level of many students it is quite important that they have some
understanding of these ideas if they use an hp 39gs to numerically evaluate limits. Because of the CAS on the
hp 40gs this situation is less likely to be a problem for that model. The solution to all problems of this type is
to simply be aware of their existence and to allow for them rather than simply accepting the results shown in
the
NUM view.
82
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