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!

Homework Help: Epsilon Delta Proof

  1. Sep 5, 2012 #1
    1. The problem statement, all variables and given/known data

    lim 3 as x->6
    lim -1 as x->2

    2. Relevant equations

    In the first weeks of a calculus class and doing these epsilon delta proofs.

    As i am looking at two of the problems i have been assigned:

    Lim 3 as x->6
    Lim -1 as x->2

    3. The attempt at a solution
    considering both are horzontal lines, if i give some ε then there is no intersection with the function and thus no δ. ε must be > 0 so not sure how our proof statement will work:

    Given ε>0, choose δ=ε. If 0<0<δ, then |0|<δ, then |3-3| = |0| < δ=ε thus |3-3|<ε whenever 0<|0|<δ. Therefore, by the definition of a limit, lim 3 = 3 as x->6
  2. jcsd
  3. Sep 5, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Hello freezer. Welcome to PF !

    One comment first: For a constant function, you can pick anything for δ, often just choose δ = 1.

    Now for your proof. What is the general ε - δ formulation for limx → a f(x) = L ?

    For any ε > 0, there exists a δ such that for any x for which 0 < |x - a| < δ, then |f(x) - L| < ε .

    You don't have any x the following statement of yours.
    ... If 0<0<δ, then |0|<δ, then |3-3| = |0| < δ ...​
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook