The following function is defined for all , and is a positive integer. Prove or provide a counterexample to the following statement.
Assume exists for all and is bounded,
for some constant for all . Then,
Incomplete.
The following function is defined for all , and is a positive integer. Prove or provide a counterexample to the following statement.
Assume exists for all and is bounded,
for some constant for all . Then,
Incomplete.
Counterexample. Let . Then, , and for all . From a prior counterexample (exercise 22), we know that although the sequence converges to zero, the infinite integral
diverges.