Wednesday, November 29, 2006

More on Limits

Finding the limit of f(x) as x approaches infinity is simple. Memorize the behaviors of the generic equation types:

higher degree/lower degree = No limit.
lower degree/higher degree = 0.
same degree/same degree = coefficient/coefficient.

If substitution produces a non-zero/zero, there is no limit and instead there is a vertical asymptote.
A hole occurs when the initial substitution produces zero/zero.

The following are the numbers to put outside of the box for given denominators in cases where synthetic division is possible:
(4-x) --> 4
(x-4) --> 4
(x+4) --> -4

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