Please, tell me which of these are true (and why):
1. Every unbounded sequence is divergent.
2. Every convergent sequence is bounded.
3. A decreasing sequence is convergent if and only if it is bounded above.
4. The arcsin function is increasing an concave downward on the interval <-1,0>.
5. If a function is continuous on the interval I, then it is integrable over I.
6. Differentiability is the sufficient but not necessary condition for integrability.
And I cannot find what the frontier is.
Let P be a frontier point of the set A. Then
[A] P is in A, [B] P is the member of the closure of A, [C] P is in A', [D] every neighborhood of P contains at least one element of A and at least one element of A'
Thanks in advance!