# Urgent!!

• Apr 30th 2007, 01:14 PM
miss_lolitta
Urgent!!
can someone help me to prove that:

if y(t)> 0 and increasing function then:

y(t) tends to infinite as t tends to infinite ??!

• Apr 30th 2007, 02:36 PM
Plato
Quote:

Originally Posted by miss_lolitta
can someone help me to prove that:
if y(t)> 0 and increasing function then:
y(t) tends to infinite as t tends to infinite ??!

Of course, the proposition is false.

Consider y(t)=arctan(t)+pi/2.
The function y is certainly positive and increasing.
If fact it is a very, very well behaved function.
But the function y is bounded above by pi.
• Apr 30th 2007, 02:44 PM
TD!
I deleted my stupid reply, amazing how one can be deceived by a false statement :D
• May 1st 2007, 08:56 AM
miss_lolitta
just!!i wona to tell u that :

y(t) is not a boundedhttp://www.bigsmileys.com/images/def...4/wow-girl.gif

thans for all
• May 1st 2007, 09:11 AM
TD!
Now that makes more sense and it would've made my "proof" valid.

So we have y(t) > 0, increasing and unbounded. For the function not to diverge (go to infinity), it would have to converge to a real value or oscillate. It cannot oscillate since it's increasing, y(b) > y(a) for every b > a. It can't converge to a real value (say L) either, since that would make it bounded (by L).