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Find the limit of this function

  1. Apr 25, 2008 #1
    Hey there

    Find the lim of F(X) as X approaches zero

    F(X) = 0/X ( Zero over X )

    Thanks.
     
  2. jcsd
  3. Apr 25, 2008 #2

    Gib Z

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    Well its a constant function equal to 0 for all values of x not equal to zero. So we can see the limit is equal to 0.
     
  4. Apr 25, 2008 #3

    exk

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    You could also use l'Hopital and get the same answer as Gib_Z provided.
     
  5. Apr 25, 2008 #4
    Yeah it is zero but I want the lim without L'Hopital rule, I want the solution using Algebra.
     
  6. Apr 25, 2008 #5
    Find the Lim of 0/X as X approaches zero.

    0/X = X-X/X = X/X - X/X = 1-1 = 0
     
  7. Apr 25, 2008 #6

    exk

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    alternatively you can say that if y is a member of the the Reals then 0*y=0 set y=1/x. While not wrong, your solution simply overcomplicates things.
     
  8. Apr 26, 2008 #7
    no matter what x is, the answer will always be 0. unless x = 0, then it is undefined. so you can say it is just approaching 0
     
  9. Apr 27, 2008 #8

    HallsofIvy

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    f(x) approaches L as x goes to a if and only if f(x_n) approaches L for any sequence of numbers x_n approaching a.

    Let x_n be any sequence of numbers approaching 0. What is 0/x_n? What is the limit of that sequence.
     
  10. Apr 27, 2008 #9
    I don't know anything about Sequence limits.
     
  11. Apr 27, 2008 #10

    Gib Z

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    But you ask of the limit of continuous functions?
     
  12. Apr 27, 2008 #11
    Do you know the definition of a limit? If so it is obviously zero.
     
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