Limit supreme solve i am not able to

[rishikesh86]

limit supreme...please 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



please solve i am not able to

 

[rishikesh86]

please ane body help me

 

[HallsofIvy]

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



please solve i am not able to

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!

 

[rishikesh86]

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

 

[Emmanuel114]

For what class?

 

[rishikesh86]

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

 

[rishikesh86]

please help me

 

[HallsofIvy]

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.

 

[rishikesh86]

thanx for the help