Limit as x approaches infinity [(x+1)/(x-1)]^x
I divided everything by an x. I see that the numerator would be e; but not too sure what to do or if that is the right process.
Help
I am going to find the limit of,Originally Posted by Nichelle14
. I will assume that it exists, (I will leave that to you to prove).
Begin by saying the limit exists,
Thus, (using the concept of countinous functions)
Using, the properties of logarithms,
Since, it is expressable as a Taylor polynomial,
Thus,
Open parantheses,
Since, each term with and "x" gives a zero you have,
Thus,
Finally,
---
Thus, given,
Divide by "x" as you said,
Since the numerator and denominator (non-zero) both exist you can conclude that the limit is,
Hello, Nichelle14!
You were on the right track . . .
Inside the parentheses, divide top and bottom by
. . So we have: .
You recognized that the numerator is . . . good!
But did you know that the denominator is ? **
Therefore, the limit is: .
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**
A very handy theorem: .