1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Epsilon Delta

  1. Apr 13, 2013 #1

    Zondrina

    User Avatar
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    HI Zondrina! :smile:

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

    Zondrina

    User Avatar
    Homework Helper

    Thanks tim, cleaned up nicely :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Epsilon Delta
  1. Epsilon delta (Replies: 1)

  2. Epsilon and delta (Replies: 3)

  3. Delta epsilon proof (Replies: 5)

Loading...