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Peicewise limit help

  1. Sep 13, 2005 #1
    F(x)= 2x^2, x<1
    3, X=1
    X+, x>1

    Find

    lim(x-->1) f(X)

    f(1)=

    not exactly sure how to do this. would not f(1) be just 3, since it is defined as that in the function. I am not sure about how to take that limit.

    Thanks
     
  2. jcsd
  3. Sep 13, 2005 #2

    LeonhardEuler

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    Gold Member

    When it comes to the limit of a function at x=a, the value of the function at a is irrelevant. In fact the function may not even be defined at "a", but the limit could still exist. So the fact that f(1)=3 is irrelevant to the problem. When looking for the limit, we must find a number that the function gets very close to as x approaches "a". It must get close to the same number when approaching from the left or right, or else the limit does not exist. In the case of this function, I think you might have made an error in typing it when you said that F(x) is equal to "X+" for x>1. But whatever it is, just see what number the function gets close to as x gets close to 1 from the right and the left. If they are the same number, then this is the limit; if not, then the limit does not exist.
     
  4. Sep 13, 2005 #3
    sorry that should be x+1
     
  5. Sep 13, 2005 #4
    ok so

    lim(x->1+)=(1+1)=2
    lim(x->1-)=(1+1)=2 so the limit exists, i dont understand how that helps in finding the overall limit of F(x) at 1.
     
  6. Sep 13, 2005 #5

    LeonhardEuler

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    Gold Member

    So the limit is 2. The limit is just the number the function approaches from both the left and the right.
     
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