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new new math limit
Posted:
Sep 16, 1998 1:57 PM
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Lin McMullin writes:
While all that is being said about limits from graphs and tables is true,
let's ask the same questions with one added "Given," namely the equation.
If you are given (1) the equation for a function, for example f(x) = 2xe^(2x)
(AB 1998 #2) and (2) asked to find the limit (x --> infinity, or finite).
Is there a problem with making a graph or table with a calculator or computer
and "finding" the limit from it?
IMHO: No. The student by the end of a good precalculus course and or shortly
into a calculus course should know that this particular function has no
problem points (is not pathological) and therefore the value of the limit on a
graph or table, at infinity or some finite point, is what is seems to be.
[rest snipped]
The student should SAY that this function is continuous, and thus that
the lim x->a of f(x) is just f(a).
Similarly for the limits as x -> infinity .. they can say something
about the end behavior and how they know what it will do.
Just making a table showing f(big number) = really big number
shouldn't be quite sufficient, in my opinion. Maybe 3/4 credit or so
on the AP test.
--Joshua Zucker
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