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.

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- July 5th 2006, 04:54 PMNichelle14How do I find this limit
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 - July 5th 2006, 05:27 PMThePerfectHackerQuote:

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,

- July 5th 2006, 05:48 PMSoroban
Hello, Nichelle14!

You were on the right track . . .

Quote:

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: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

******

A*very*handy theorem: .