Finding the limit of a function with e and ln

  • Context: Undergrad 
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    Function Limit Ln
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Discussion Overview

The discussion revolves around finding the limit of the function \((e^x + x)^{(1/x)}\) as \(x\) approaches infinity. Participants explore different methods to arrive at the limit, including the use of natural logarithms and direct factoring.

Discussion Character

  • Mathematical reasoning, Homework-related

Main Points Raised

  • One participant asks for help in finding the limit as \(x\) approaches infinity for the expression \((e^x + x)^{(1/x)}\).
  • Another participant claims the limit is "e" and suggests using the property that the limit and the natural logarithm commute.
  • A participant requests further clarification on how to derive the answer of "e".
  • One participant indicates they have understood the solution after receiving help.
  • Another participant proposes an alternative method that involves factoring out \(e^x\) and using the definition of "e" to find the limit directly.

Areas of Agreement / Disagreement

There is no consensus on the methods used to find the limit, as participants present different approaches without resolving which is preferable.

Contextual Notes

Some assumptions about the behavior of the function as \(x\) approaches infinity may not be explicitly stated, and the discussion does not fully explore the implications of the different methods proposed.

trap
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lim as x->infinity [e^x + x] ^(1/x)

Can anyone help me on this please, thanks.
 
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The limit is "e"...To convince yourself,use the fact that the limit & the natural logarithm commute.

Daniel.
 
can you take me one step further than that, to get the answer e?
 
i got it now, thanks for the help
 
There would be another way to do it,directly,without use of [itex]ln[/itex].Just factor e^{x} and then use the definition of "e":
[tex]\lim_{u\rightarrow +\infty}(1+\frac{1}{u})^{u}=e[/tex]

Daniel.
 

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