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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