1961 AHSME Problems/Problem 34
Problem
Let S be the set of values assumed by the fraction .
When
is any member of the interval
. If there exists a number
such that no number of the set
is greater than
,
then
is an upper bound of
. If there exists a number
such that such that no number of the set
is less than
,
then
is a lower bound of
. We may then say:
Solution
This problem is really finding the range of a function with a restricted domain.
Dividing into
yields
. Since
, as
gets larger,
approaches
, so
approaches
as
gets larger. That means
. Since
can never be
,
can never be
, so
is not in the set
.
For the smallest value, plug in in
to get
, so
. Since plugging in
results in
,
is in the set
.
Thus, the answer is .
See Also
1961 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 33 |
Followed by Problem 35 | |
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