Page 2 of 2 FirstFirst 12
Results 16 to 21 of 21

Math Help - Evaluate a Limit

  1. #16
    Member
    Joined
    Apr 2008
    Posts
    123
    Quote Originally Posted by Jose27 View Post
    The problem is, Wolfram Alpha is calculating the limit in the complex plane with the definition I first gave, but by what I understood the limit that was asked ignores this and uses only the fact negative numbers have odd roots (ie. we want the limit of a sequence, not the limit of the function)
    Actually, the domain of x isn't specified, so I'm a little confused as well. It's actually a question from Wade's Introduction to Analysis (4th Ed), and the answer given is 1. It does seem that it's the sequence it's referring to, then?
    Follow Math Help Forum on Facebook and Google+

  2. #17
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    Quote Originally Posted by h2osprey View Post
    Actually, the domain of x isn't specified, so I'm a little confused as well. It's actually a question from Wade's Introduction to Analysis (4th Ed), and the answer given is 1. It does seem that it's the sequence it's referring to, then?
    I don't know. If the book says the solution is 1 then it can't be the sequence since that one converges to -1, but otherwise it wouldn't make sense writing x ->0+. I'm confused.
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Jose27 View Post
    I don't know. If the book says the solution is 1 then it can't be the sequence since that one converges to -1, but otherwise it wouldn't make sense writing x ->0+. I'm confused.
    The book probably made the same mistake I did.
    Follow Math Help Forum on Facebook and Google+

  4. #19
    Member
    Joined
    Apr 2008
    Posts
    123
    Quote Originally Posted by mr fantastic View Post
    (\ln x)^x = e^{\ln (\ln x)^x} = e^{x \ln (\ln x)}. So you should first consider \lim_{x \rightarrow 0^+} x \ln (\ln x) = \lim_{x \rightarrow 0^+}\frac{\ln (\ln x) }{\frac{1}{x}} which has the indeterminant form \frac{\infty}{\infty}. Using l'Hopitals rule is an obvious thing to do.
    Sorry, I'm not getting how you might get the answer 1 from this?

    I thought you couldn't use L'Hopital's on this \lim_{x \rightarrow 0^+}\frac{\ln (\ln x) }{\frac{1}{x}} as the numerator is undefined, and hence I don't see how you arrive at the indeterminate form \frac{\infty}{\infty}.
    Follow Math Help Forum on Facebook and Google+

  5. #20
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by h2osprey View Post
    Sorry, I'm not getting how you might get the answer 1 from this?

    I thought you couldn't use L'Hopital's on this \lim_{x \rightarrow 0^+}\frac{\ln (\ln x) }{\frac{1}{x}} as the numerator is undefined, and hence I don't see how you arrive at the indeterminate form \frac{\infty}{\infty}.
    Read my previous post! I made a mistake (sheesh, if the whole world didn't know, it does now)!
    Follow Math Help Forum on Facebook and Google+

  6. #21
    Member
    Joined
    Apr 2008
    Posts
    123
    Quote Originally Posted by mr fantastic View Post
    Read my previous post! I made a mistake (sheesh, if the whole world didn't know, it does now)!
    Ah, got it. Sorry for the confusion
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. [SOLVED] Evaluate the limit
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 1st 2011, 10:39 PM
  2. evaluate the limit
    Posted in the Calculus Forum
    Replies: 7
    Last Post: October 12th 2010, 06:24 PM
  3. Evaluate the limit
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 17th 2010, 10:59 AM
  4. Evaluate the limit
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 17th 2010, 09:00 AM
  5. Evaluate Limit
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 5th 2008, 10:09 AM

Search Tags


/mathhelpforum @mathhelpforum