# Help me find a limit!

1. Sep 20, 2010

### wumple

1. The problem statement, all variables and given/known data
Find the limit of e(-t/2)((k/2)t+c) as t approaches infinity where k and c are constants

2. Relevant equations
Not sure..?

3. The attempt at a solution
Plugging in t = infinity gives me an indeterminate form, and multiple applications of L'hopital's rule have led me no where. Any suggestions? I can see graphically that it goes to 0, but I'm not sure how to show this analytically. I can see that if I expand it, the e(-t/2)c term goes to zero, but I'm not sure about the other term.

2. Sep 20, 2010

### rock.freak667

I do not know if this is a valid form of proving limits, but e-t/2 approaches 0 faster than any polynomial can approach infinity as t→∞.

3. Sep 20, 2010

### wumple

yeah I was hoping that L'hopital's rule would show that but it didn't work out...

4. Sep 20, 2010

### rock.freak667

Wouldn't L'Hopital's rule as show it going to zero since d/dt{0.5kt+c} is does not contain a tern in 't'?

5. Sep 20, 2010

### wumple

Oops! yes! Thank you, I found my mistake.