Limit of e(-t/2)((k/2)t+c) as t Approaches Infinity

[wumple]

Homework Statement

Find the limit of e^(-t/2)((k/2)t+c) as t approaches infinity where k and c are constants

Homework Equations

Not sure..?

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.

 

[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→∞.

 

[wumple]

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

 

[rock.freak667]

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

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'?

 

[wumple]

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'?

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