Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Could someone help me with this limit problem? ?

I am not sure how the answer is obtained. I do know that the 

limit (as n->infinity) of (1+ (1/n))^n is e^x

but I am finding it difficult to manipulate the answer with this information. 

Attachment image

1 Answer

  • rotchm
    Lv 7
    2 months ago
    Favorite Answer

    First, "n->infinity of (1+ (1/n))^n is e^x ". NO it is not.

    n->infinity of (1+ (1/n))^n is e. 

    Let's ignore the t since it really has nothing to do with it.

    (1+r/n)^n = (1+1/(n/r))^n = [(1+1/(n/r))^(n/r)]^r.

    Look at the expression in brackets. Its simply e.

    (Indeed, doing the change of var n/r = u you 

    get (1+1/u)^u which gives e in the limit.)

    So,  [(1+1/(n/r))^(n/r)]^r. = e^r.

    ^t each side answers your original question. 

    I've answered you in the past and I was the first to answer and I had the good answers yet you voted other people who made mistakes. That was very dishonest of you to do so. I do hope you will be honest and grateful this time...

Still have questions? Get your answers by asking now.