Jon works in the shipping department at crunchy cereal. to find out how many cereal boxes fit in one shipping container, jon div
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1. has a horizontal asymptote at
This means that
(for at least one of these limits)
2. has a vertical asymptote at
This means that has a non-removable discontinuity at
. Since
is some rational function, there must be a factor of
in its denominator.
3. has an
-intercept at (1, 0)
This means .
(a) With
the second point above suggests . The first point tells us that
In order for the limit to be 0, the denominator's degree should exceed the numerator's degree; the only way for this to happen is if so that the linear terms vanish.
The third point tells us that
So
(b) Since
we find that , and
and
.