
Limit & Derivative help
Hi there,
I'm floundering here, and could use some insight, I have read through the paper posted regarding epsilondelta 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 deltaepsilon 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

The main strategy in limit proofs is to start with $\displaystyle \epsilon$ and try to find a formula for $\displaystyle \delta$ in terms of $\displaystyle \epsilon$. That way, we can say that
$\displaystyle \mbox{For all }\epsilon\mbox{ there exists a }\delta\mbox{ such that ...}$
For the first problem, we want to find a $\displaystyle \delta>0$ for every $\displaystyle \epsilon>0$ such that
$\displaystyle 0<xc<\delta\quad\Rightarrow\quad(mx+b)(mc+b)<\epsilon,$
which amounts to saying
$\displaystyle 0<xc<\delta\quad\Rightarrow\quadm(xc)<\epsilon.$
Can you think of a formula for $\displaystyle \delta$, expressed in terms of $\displaystyle \epsilon$, that would make the above statement true?