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Limit in the interval

  1. Jun 2, 2009 #1
    if 4-x^2 < f(x) < 4 + x^2 for x in [-1,1] then whats lim as x goes to zero of f(x) ...

    this setup looks like epsilon form .. not sure how to interpret this guy...
     
  2. jcsd
  3. Jun 3, 2009 #2
    Is it not just 4? Since f(x) is bounded by the two curves (see picture attached).

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    Last edited by a moderator: Aug 6, 2009
  4. Jun 3, 2009 #3
    double checked it. the have it right. any ideas?
     
  5. Jun 3, 2009 #4

    HallsofIvy

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    Ideas about what? You have already been told that the limit is 4. That should be obvious from the "sandwiching" property. f(x) is always between 4- x2 and 4+ x2 and they both go to 4.
     
  6. Jun 3, 2009 #5
    may be I dont understand the problem to begin with.. can you explain. thanks
     
  7. Jun 3, 2009 #6
    Just think of it intuitively. What happens to the given bounds on f as x gets smaller and smaller (approaching zero)? Don't worry about any particular theorems, if you don't understand what is going on here you need to revisit the intuitive concept of a limit.
     
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