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Delta-Epsilon Proof

  1. Sep 14, 2005 #1
    A positive number E and the limit L of a function f at a are given. Find a number d such that |f(x) - L| < E if 0 < |x-a| < d.

    Lim x --> 5 (1/x) = 1/5; E = 0.05

    The answer or value of d = 1/505.

    These are the steps that I did, and, unfortunately, my efforts did not end in that result.

    |f(x) - (1/5)| < .05 if |x-5| < d.

    a. f(5 - d_1) = (1/5) + .05 = 0.25

    1/(5 - d_1) = 0.25

    d_1 = 1

    b. f(5 + d_2) = (1/5) - 0.05 = .15

    1/(5 + d_2) = 0.15

    d_2 = 1.67

    Neither delta fits the answer. Why is my proof terribly incorrect? Is there an alternate method?

    Thanks.
     
    Last edited: Sep 14, 2005
  2. jcsd
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