Evaluate the limit as x goes to infinity using L'Hospital's rule

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Homework Help Overview

The discussion revolves around evaluating the limit of the expression 8xe^(1/x) - 8x as x approaches infinity, specifically using L'Hospital's rule. Participants are exploring the application of this rule in the context of limits involving exponential functions and algebraic manipulation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning how to apply L'Hospital's rule given the structure of the limit, particularly concerning the denominator being equal to 1. There is also discussion about rewriting the expression and the implications of factoring and using reciprocals.

Discussion Status

The discussion is ongoing, with participants providing hints and attempting to clarify the steps involved in rewriting the limit expression. Some participants are exploring different interpretations of the problem, while others are seeking to understand the reasoning behind the suggested manipulations.

Contextual Notes

There are indications of confusion regarding the application of L'Hospital's rule and the manipulation of the expression, suggesting that participants are navigating through foundational concepts related to limits and exponential functions.

Loopas
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(1)

Evaluate the limit as x goes to infinity using L'Hospital's rule:

8xe^(1/x)-8x

(2)

L'Hopital's Rule

(3)

How can I use L'Hopital's Rule for this problem if the denominator is 1? Wouldn't that just give me an undefined limit? This may be a pretty stupid question, but I'm new to this.
 
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Loopas said:
(1)

Evaluate the limit as x goes to infinity using L'Hospital's rule:

8xe^(1/x)-8x

(2)

L'Hopital's Rule

(3)

How can I use L'Hopital's Rule for this problem if the denominator is 1? Wouldn't that just give me an undefined limit? This may be a pretty stupid question, but I'm new to this.

Hint: factorise first. Also, ##x = \displaystyle \frac{1}{\frac{1}{x}}##.
 
How do you you know that x=(1)/(1/x)?
 
\frac{1}{(\frac{1}{x})}

is the reciprocal of 1/x...

ehild
 
Ahhh ok so I can rewrite as (8x(e^(1/x)-1))/(1/x)?
 
Not quite.
 
Loopas said:
Ahhh ok so I can rewrite as (8x(e^(1/x)-1))/(1/x)?

That x is replaced by the 1/(1/x) term. So why does it appear again?

Sorry no latex. On my phone at the moment.
 

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