# Limit & Derivative help

• December 10th 2009, 10:41 AM
Conorsmom
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
• December 10th 2009, 02:46 PM
Scott H
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?