How to find horizontal asymptotes?

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Homework Help Overview

The discussion revolves around finding horizontal asymptotes for the function f(x)=(8-4x)e^x. Participants are exploring the behavior of the function as x approaches positive infinity.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the possibility of rewriting the function and applying L'Hospital's Rule. There are questions about how to determine horizontal asymptotes when the function is presented in its current form.

Discussion Status

Some participants have suggested approaches involving L'Hospital's Rule, while others have pointed out that there may not be a horizontal asymptote as x approaches positive infinity. The discussion is ongoing with various interpretations being explored.

Contextual Notes

There is an acknowledgment that the original poster believes the answer is 0, but there is a lack of consensus on the existence of a horizontal asymptote as x approaches positive infinity.

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Homework Statement



f(x)=(8-4x)e^x

Homework Equations





The Attempt at a Solution



I know you can usually compare the top and bottom and determine that way but how can you do it when it's like this? I know the answer is 0 already i don't know how to get it though
 
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Do you see how you might be able to re-write this and then use L'Hospital's Rule?

Edit:
Just as a side note, I hope you realize that there is no horizontal asymptote as x goes to positive infinity.
 
Robert1986 said:
Do you see how you might be able to re-write this and then use L'Hospital's Rule?

Edit:
Just as a side note, I hope you realize that there is no horizontal asymptote as x goes to positive infinity.

ah i think i got it.

do you end up with -4/(-1/e^(-x)) which basically is equal to -4/-infinity = 4/infinity = 0?
 
Yes, but just to say it again, it is not as x goes to positive infinity.
 

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