Results 1 to 4 of 4

Math Help - squeeze theorem limit

  1. #1
    Newbie
    Joined
    Mar 2012
    From
    nz
    Posts
    4

    squeeze theorem limit

    Hello, I am trying to apply the squeeze theorem to the following:
    e^sin(pi/x)
    limit as x tends towards zero.

    -1 < e^sin(pi/x) > 1

    -(pi/x) < e^sin(pi/x) < (pi/x)

    plugging in zero to the x variables gives me a limit of zero.

    My question is, am I correct in how I have factored the (pi/x) components to the outer edges ?
    Thank you.
    Last edited by tedsauc; April 1st 2012 at 04:56 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,656
    Thanks
    1479

    Re: squeeze theorem limit

    Quote Originally Posted by tedsauc View Post
    Hello, I am trying to apply the squeeze theorem to the following:
    e^sin(pi/x)
    limit as x tends towards zero.

    -1 < e^sin(pi/x) > 1

    -(pi/x) < e^sin(pi/x) < (pi/x)

    plugging in zero to the x variables gives me a limit of zero.

    My question is, am I correct in how I have factored the (pi/x) components to the outer edges ?
    Thank you.
    While I agree that you could bound \displaystyle \begin{align*} \sin{\left(\frac{\pi}{x}\right)} \end{align*} between \displaystyle \begin{align*} -\frac{\pi}{x} \end{align*} and \displaystyle \begin{align*} \frac{\pi}{x} \end{align*}, how could you possibly let \displaystyle \begin{align*} x = 0 \end{align*} in the edges? You can't divide by 0... Exponentiating both sides won't help you either.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2012
    From
    nz
    Posts
    4

    Re: squeeze theorem limit

    thanks. That is where I am stuck. I don't know what to put into the edges. If anyone can offer suggestions that would be most appreciated.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,656
    Thanks
    1479

    Re: squeeze theorem limit

    Quote Originally Posted by tedsauc View Post
    thanks. That is where I am stuck. I don't know what to put into the edges. If anyone can offer suggestions that would be most appreciated.
    The fact is that the limit doesn't exist. limit Exp&#91;Sin&#91;Pi&#47;x&#93;&#93; as x to 0 - Wolfram|Alpha
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Squeeze Theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 8th 2010, 04:00 PM
  2. Evaluate the limit using the squeeze theorem?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 17th 2009, 12:03 PM
  3. Squeeze Theorem Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 8th 2009, 12:14 PM
  4. Squeeze Theorem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 28th 2009, 09:39 PM
  5. Using the Squeeze Theorem to find a limit.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 27th 2008, 11:14 PM

Search Tags


/mathhelpforum @mathhelpforum