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Homework Help: Limits of a picewise function?

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data

    We're given a piecewise function

    g(x) = {
    x if x < 1
    3 if x = 1
    2-x^2 if 1<x<=2
    x-3 if x > 2

    and were asked: lim x-> 2-

    2. Relevant equations

    2-x^2 if 1<x<=2
    x-3 if x > 2

    3. The attempt at a solution

    when i drew it out i was getting that the answer is -2 but the workbook says the answer is zero. times have occured where the answers in this workbook have been wrong, so i would just like someone to verify either one. any help is much appreciated, thanks.
  2. jcsd
  3. Apr 14, 2012 #2
    2-x^2 if 1<x<=2 Is all you really need to solve this.. As x approaches 2 from the left, the answer is -2. The other limit = -1 anyway so I don't see how they got 1.

    EDIT: They may have thought it's (2-x)^2.. That limit as x->2 is 0..
  4. Apr 14, 2012 #3


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    You may have neglected to include the parentheses.

    [itex]\displaystyle \lim_{x\to2^-}\left(2-x^2\right)=-2[/itex]

    [itex]\displaystyle \lim_{x\to2^-}\left((2-x)^2\right)=0[/itex]
  5. Apr 15, 2012 #4
    thanks to both! and nope, book def. says '(2-x^2) and not (2-x)^2, must be a printing error either in book or ans. key, but thank you!
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