Limit supreme solve i am not able to

1. Sep 16, 2007

rishikesh86

limit supreme...plz solve i am not able to

$$\limsup{t\rightarrow {\infty}} \int{p(s)ds} >1$$
and limit of integral are $$t-\tau$$ to $$t$$ where
$$\tau$$>0

plz solve i am not able to

2. Sep 16, 2007

rishikesh86

3. Sep 16, 2007

HallsofIvy

Staff Emeritus
It bothers you that someone did not answer in 4 minutes. We are not payed to sit at computers waiting to answer questions you know!

In any case, what exactly is your question? Obviously the limit will depend on exactly what p(t) is!

4. Sep 17, 2007

rishikesh86

sorry bt the quetion was given exactly asit is to me as an assignment

5. Sep 17, 2007

Emmanuel114

For what class?

6. Sep 18, 2007

rishikesh86

for maths class, i am in an technical college 2nd year

7. Sep 18, 2007

rishikesh86

plz help me

8. Sep 18, 2007

HallsofIvy

Staff Emeritus
There is no help we can give without knowing p! For example,
$$\int_{t-\tau}^t \frac{1}{t}dt= ln(t)-ln(t-\tau)= ln\left(\frac{t}{t-\tau}\right)= ln\right(\frac{1}{1-\frac{\tau}{t}}\right)$$
which has limit ln(1)= 0 as t goes to infinity but
$$\int_{t-\tau}^t t dt= \frac{1}{2}(t^2- (t-\tau)^2= \frac{1}{2}(-2t\tau +\tau^2)$$
which has no limit as t goes to infinity.

9. Sep 21, 2007

rishikesh86

thanx for the help