# stating true sentences

• May 30th 2008, 03:14 AM
marcopolon2
stating true sentences
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'

• May 30th 2008, 10:04 AM
ThePerfectHacker
Quote:

Originally Posted by marcopolon2
1. Every unbounded sequence is divergent.

If a sequence is convergent then it is bounded. Now take the contrapositive statement.
Quote:

2. Every convergent sequence is bounded.
Take $a_n = -n$.