Results 1 to 4 of 4
Like Tree2Thanks
  • 2 Post By HallsofIvy

Math Help - A few limit problems

  1. #1
    Member maxpancho's Avatar
    Joined
    Jun 2014
    From
    Mathville
    Posts
    170
    Thanks
    26

    Question A few limit problems

    1. $\lim_{x \to 0^+} \sqrt{\dfrac{1}{x}+2} - \sqrt{\dfrac{1}{x}}$

    2. $\lim_{x \to 0^+} \dfrac{\sqrt{2-x^2}}{x}$

    3. $\lim_{x \to 0} x \sin (\dfrac{1}{x})$

    Don't know how to solve. Can someone help?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466

    Re: A few limit problems

    For the first use (a- b)\frac{a+ b}{a+ b}= \frac{a^2- b^2}{a+ b}. Then multiply both numerator and denominator by \sqrt{x}.

    For the second, write it as \sqrt{\frac{2- x^2}{x^2}}

    For the third, -1\le sin(1/x)\le 1.
    Thanks from romsek and maxpancho
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member maxpancho's Avatar
    Joined
    Jun 2014
    From
    Mathville
    Posts
    170
    Thanks
    26

    Re: A few limit problems

    First:
    $\lim_{x \to 0^+} \dfrac{\dfrac{1}{x}+2-\dfrac{1}{x}}{\sqrt{\dfrac{1}{x}+2}+\sqrt{\dfrac{1 }{x}}}

    = \lim_{x \to 0^+} \dfrac{2\sqrt{x}}{\sqrt{1+2x}+1}

    = \lim_{x \to 0^+}\dfrac{0}{2}=0
    $

    Second:

    $\lim_{x \to 0^+}\sqrt{\dfrac{2- x^2}{x^2}}$

    Conclude that the limit does not exist, because I can't manipulate the expression any more?

    Third:

    Still confused.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member maxpancho's Avatar
    Joined
    Jun 2014
    From
    Mathville
    Posts
    170
    Thanks
    26

    Re: A few limit problems

    Also, regarding the second problem. Is it DNE or undefined? The answer in my book was DNE, but I don't see why it can't be just undefined. What's the difference?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Limit help (two problems)
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 19th 2011, 02:25 PM
  2. Two limit problems
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 8th 2009, 03:55 PM
  3. 4 Limit problems.
    Posted in the Calculus Forum
    Replies: 11
    Last Post: October 2nd 2008, 09:33 AM
  4. limit problems
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 6th 2008, 08:19 PM
  5. Limit Problems
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 5th 2007, 03:09 AM

Search Tags


/mathhelpforum @mathhelpforum