Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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).


    Attached Files:

    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


    User Avatar
    Science Advisor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook