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Sqareroot limit proof

  1. Sep 25, 2007 #1
    square root limit proof

    R is the real nmbers

    so let A be in R
    let f: A -> R be such that f(x)>0 for all x in A
    c is in A

    Does any one know the proof to or even get me started on this proof shown below

    [It's hard to write roots on the computer, so I will use the 1/2-th power instead.] SO i want to prove the following

    lim x ->c [f(x)^(1/2)] = [lim x->c f(x)]^(1/2),
    PROVIDED f(x) > 0
     
    Last edited: Sep 25, 2007
  2. jcsd
  3. Sep 25, 2007 #2
    Use the continuity of the square root and the definition of limit.
     
  4. Sep 25, 2007 #3

    HallsofIvy

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    In other words, this function, f, has very little to do with the question. The definition of "h(x) is continuous at x=a" is lim(x->a) f(x)= f(a). In this case, what is a?
     
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