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Homework Help: Epsilon Delta

  1. Apr 13, 2013 #1

    Zondrina

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    1. The problem statement, all variables and given/known data

    Suppose f is a function defined on a set ##S## in ##ℝ^n## and suppose ##Q## is a limit point of ##S##.

    If ##f(P) → 3## as ##P → Q## prove from first principles that ##\frac{1}{f(P)} → \frac{1}{3}## as ##P → Q##.

    2. Relevant equations



    3. The attempt at a solution

    I'm a bit rusty with these.

    I know : ##\forall ε'>0, \exists δ'>0 \space | \space 0 < |P-Q| < δ' \Rightarrow |f(P) - 3| < ε'##

    I want : ##\forall ε>0, \exists δ>0 \space | \space 0 < |P-Q| < δ \Rightarrow |1/f(P) - 1/3| < ε##

    For some reason I'm blanking on what to do next.
     
  2. jcsd
  3. Apr 13, 2013 #2

    tiny-tim

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    HI Zondrina! :smile:

    Hint: |1/f(P) - 1/3| = |f(P) - 3| / |f(P)| :wink:
     
  4. Apr 13, 2013 #3

    Zondrina

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    Thanks tim, cleaned up nicely :)
     
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