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

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Homework Help Overview

The problem involves finding the limit of the expression e-t/2((k/2)t+c) as t approaches infinity, where k and c are constants. The original poster expresses uncertainty about the appropriate methods to use, particularly in relation to L'Hôpital's rule and the behavior of the exponential term compared to polynomial growth.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of L'Hôpital's rule and its effectiveness in resolving the limit. There is a consideration of the indeterminate form encountered when substituting t with infinity. Some participants question the validity of their approaches and the assumptions regarding the rates at which the exponential and polynomial terms approach their limits.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the limit and the effectiveness of L'Hôpital's rule. Some guidance has been offered regarding the behavior of the exponential term relative to polynomial terms, but no consensus has been reached on a definitive solution.

Contextual Notes

There is mention of an indeterminate form and the challenges faced when applying L'Hôpital's rule. Participants are also considering the graphical behavior of the function as t approaches infinity.

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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.
 
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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→∞.
 
yeah I was hoping that L'hopital's rule would show that but it didn't work out...
 
wumple said:
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'?
 
rock.freak667 said:
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.
 

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