Results 1 to 4 of 4

Math Help - When a limit is equal to a number...

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    51

    When a limit is equal to a number...

    what is that number ... like if we had a limit that was equal to 3 is 3 the point where the graph is undefined??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by yess View Post
    what is that number ... like if we had a limit that was equal to 3 is 3 the point where the graph is undefined??
    I find this to be a very strange question.. incoherent really. Maybe you should go back and review the definition of limit?

    Graphical explanation may help. On the left is graph of f(x)=x. On right is graph of

    f(x)=\begin{cases} x&,\ x\ne2\\ 4&,\ x=2\end{cases}

    On the left we have \displaystyle \lim_{x\to2}f(x)=2 and \,f(2)=2. On the right we have \displaystyle \lim_{x\to2}f(x)=2 and \,f(2)=4.
    Attached Thumbnails Attached Thumbnails When a limit is equal to a number...-limcont.png  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2010
    Posts
    51
    Quote Originally Posted by undefined View Post
    I find this to be a very strange question.. incoherent really. Maybe you should go back and review the definition of limit?

    Graphical explanation may help. On the left is graph of f(x)=x. On right is graph of

    f(x)=\begin{cases} x&,\ x\ne2\\ 4&,\ x=2\end{cases}

    On the left we have \displaystyle \lim_{x\to2}f(x)=2 and \,f(2)=2. On the right we have \displaystyle \lim_{x\to2}f(x)=2 and \,f(2)=4.
    so like when we say "the limit is 4" that means the graph is discontinuous at x=4??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by yess View Post
    so like when we say "the limit is 4" that means the graph is discontinuous at x=4??
    No.

    Referring to the graphs in my first post: for the left one, f(x) is continuous at x=2 because

    1) the limit of f(x) as x approaches two exists
    2) that limit is equal to the value of f at that point.

    In symbols, \displaystyle \lim_{x\to2}f(x)=f(2).

    The graph on the right is discontinuous at x=2 because, although the limit exists, it does not equal the value of the function at that point.

    Informally continuity is often described as "it's continuous if you can draw it without lifting your pen," and applying that to the graph on the right, it is not continuous at x=2 because the function "jumps" and you have to lift your pen there.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Why does this limit equal e?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 29th 2009, 05:37 PM
  2. Replies: 1
    Last Post: November 22nd 2009, 06:32 PM
  3. Replies: 7
    Last Post: November 16th 2009, 06:07 PM
  4. strange limit equal to second derivative?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 23rd 2009, 07:32 PM
  5. limit equal to 0?
    Posted in the Calculus Forum
    Replies: 15
    Last Post: January 13th 2008, 10:10 AM

Search Tags


/mathhelpforum @mathhelpforum