Results 1 to 2 of 2

Math Help - Limit & Derivative help

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    15

    Limit & Derivative help

    Hi there,

    I'm floundering here, and could use some insight, I have read through the paper posted regarding epsilon-delta proofs, but I'm having trouble swallowing the information. Perhaps it's been too long since I took Calc courses, and maybe I should buy one of those Calc for dummies books I apreciate any help you can give.

    ** Use the formal delta-epsilon definition of
    lim f(x) = L to prove that
    x -> a
    lim (mx+b) = mc+b
    x->c


    **Use the definition of the derivative to prove that
    D (mx + b)=m
    ..x

    and discuss the relationship of definite integral to the derivative
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    319
    The main strategy in limit proofs is to start with \epsilon and try to find a formula for \delta in terms of \epsilon. That way, we can say that

    \mbox{For all }\epsilon\mbox{ there exists a }\delta\mbox{ such that ...}

    For the first problem, we want to find a \delta>0 for every \epsilon>0 such that

    0<|x-c|<\delta\quad\Rightarrow\quad|(mx+b)-(mc+b)|<\epsilon,

    which amounts to saying

    0<|x-c|<\delta\quad\Rightarrow\quad|m(x-c)|<\epsilon.

    Can you think of a formula for \delta, expressed in terms of \epsilon, that would make the above statement true?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 16
    Last Post: November 15th 2009, 05:18 PM
  2. a derivative and 1 limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 2nd 2009, 04:54 PM
  3. Limit and Derivative....Help
    Posted in the Calculus Forum
    Replies: 12
    Last Post: February 21st 2009, 12:57 AM
  4. using limit derivative?
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 10th 2008, 10:42 PM
  5. Derivative/limit
    Posted in the Calculus Forum
    Replies: 7
    Last Post: October 13th 2008, 03:07 PM

Search Tags


/mathhelpforum @mathhelpforum