Results 1 to 5 of 5

Math Help - Limit Problem

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    9

    Limit Problem

    Calculate the following limit

     \lim_{x \to 0} \ (x^2) cosh (1/x)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    715
    when x tends to 0 ,  x^2 \cosh(\frac{1}{x}) tends to infinity .

    Since  \cosh(x) = \frac{1}{2}( e^x + e^{-x} )

    when x tends to infinity ,

     \cosh(x) = \frac{e^x}{2}

    we'll have  \lim_{x\to\infty} 2 \frac{e^x}{x^2} = \infty
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2009
    Posts
    9
    im sorry but i dont really get what u mean.

    how does the coshx = e^x / 2 come about ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Aug 2009
    Posts
    130
     coshx = \frac{e^x + e^{-x}}{2} . Let x tend to infinity and the  e^{-x} \rightarrow 0 , while the rest of the expression increases beyond all bounds. The  x^2 also increases beyond all bounds, which is why the entire expression approaches infinity.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Aug 2009
    Posts
    9
    Quote Originally Posted by simplependulum View Post
    when x tends to 0 ,  x^2 \cosh(\frac{1}{x}) tends to infinity .

    Since  \cosh(x) = \frac{1}{2}( e^x + e^{-x} )

    when x tends to infinity ,

     \cosh(x) = \frac{e^x}{2}

    we'll have  \lim_{x\to\infty} 2 \frac{e^x}{x^2} = \infty

    okay ive got that. but how did the  2 \frac{e^x}{x^2} = \infty come about ?

    Thanks for the help guys
    Last edited by defcon3; August 19th 2009 at 10:33 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: August 13th 2010, 01:03 AM
  2. Replies: 1
    Last Post: August 8th 2010, 11:29 AM
  3. Another Limit Problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 30th 2010, 01:19 AM
  4. Limit, Limit Superior, and Limit Inferior of a function
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 3rd 2009, 05:05 PM
  5. Limit Problem
    Posted in the Calculus Forum
    Replies: 10
    Last Post: March 20th 2007, 11:54 AM

Search Tags


/mathhelpforum @mathhelpforum