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 ??!


thanks in advance,,

Quote:

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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 ??!

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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.

I deleted my stupid reply, amazing how one can be deceived by a false statement :D

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

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).