Problem: Let be the set of values assumed by the function 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 no number of the set is less than , then is a lower bound of . We may then say:
Answer Choices:
A. is in is not in
B. is in is not in
C. both and are in $S
D. neither nor is in
E. does not exist either in or outside
Solution:
Let . From the form we see that increases as increases for all . Thus the smallest value of is obtained when and is in .
As continues to increase approaches but never becomes equal to . and is not in .