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Math Help - Graph this piecewise function and use it to determine the values of a for which the l

  1. #1
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    Question Graph this piecewise function and use it to determine the values of a for which the l

    \begin{displaymath}<br />
   f(x) = \left\{<br />
     \begin{array}{lr}<br />
2-x   &  if      x<-1\\<br />
x    & if          -1<=x<1\\<br />
(x-1)^2 &    if     x>=e1       <br />
     \end{array}<br />
   \right.<br />
\end{displaymath}
    I'm supposed to graph this piecewise function and use it to determine the values of a for which the limit of f(x) exists as x approaches a.


    I'm not entirely sure how to start this question. Looking on the graph I'm thinking the only place where the limit of f(x) as x approaches a doesn't exist is -1 and 1. Could someone please explain?
    That is the graph. So does the limit of f(x) as x approaches a exist everywhere except 1 and -1 ?
    Last edited by iamanoobatmath; September 27th 2010 at 11:17 PM.
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by iamanoobatmath View Post
    \begin{displaymath}<br />
   f(x) = \left\{<br />
     \begin{array}{lr}<br />
2-x   &  if      x<-1\\<br />
x    & if          -1<=x<1\\<br />
(x-1)^2 &    if     x>=e1       <br />
     \end{array}<br />
   \right.<br />
\end{displaymath}
    I'm supposed to graph this piecewise function and use it to determine the values of a for which the limit of f(x) exists as x approaches a.


    I'm not entirely sure how to start this question. Looking on the graph I'm thinking the only place where the limit of f(x) as x approaches a doesn't exist is -1 and 1. Could someone please explain?
    That is the graph. So does f(x) exist everywhere 1 and -1
    Well, f(x) is defined over all the reals, but \displaystyle\lim_{x\to a}f(x) does not exist at a=-1 and a=1 as you said. There's really not a lot to it. (If you want some more detail: at those points left and right limits exist, but they are not equal.) Nice presentation with LaTeX and graph.
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  3. #3
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    Quote Originally Posted by undefined View Post
    Nice presentation with LaTeX and graph.
    Wolframlpha is a life safer when the bloody textbook and the solution manual only gives answers to odd questions.

    Nice name, btw.
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