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Unformatted text preview: 80 1 Solutions 35.
with 40. and . Thus, and with 41. with . But since, for any natural number ,
lower degree terms. Thus translating
the highest power of found in
will produce the same highest power
. Since the same is also true for
, it follows that
. Thus, is a proper rational function.
42. If then where . Then and
is a proper rational function.
but not in
does not have a factor of
rule we have Thus . Then we can write
. By the quotient . Suppose
. Then the numerator
has a factor of . But this implies has a factor of . But this
is impossible since
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
- Fall '08