quick question

R

Ryan Rigdon

Junior Member
Joined
Jun 10, 2010
Messages
246
how do i get my problems to post like a workled out math problem in a book. i am having trouble with a proof.
 
Give an E-(snake looking symbol) proof of lim (x^2-2x-4) = 4.

the limit as x approaches -2
 
That is an epsilon-delta proof. That snake looking symbol is the lowercase Greek letter delta, \(\displaystyle {\delta}\)

\(\displaystyle \epsilon-\delta\) proof of \(\displaystyle \lim_{x\to\ -2}(x^{2}-2x-4)\)

This can be a tough concept to wrap ones head around when one is new to the topic. It takes something that is otherwise intuitive and turns it

into a rigorous, confusing mess.

There is plenty ot there to Google on the topic. Google epsilon delta proof of limit and you will find lots. YouTube has nice videos on it.

Anyway,

\(\displaystyle |(x^{2}-2x-4)-4|=|x^{2}-2x-8|=|x-4||x+2|\)

We want to restrict \(\displaystyle \delta\) so that \(\displaystyle {\delta}\leq 1\), so that:

\(\displaystyle |x-4|<1\)

\(\displaystyle 1<x<5\)

\(\displaystyle 1<x+2<5\)

\(\displaystyle 3<x<7\)

\(\displaystyle |x+2|<7\)

\(\displaystyle |x+2||x-4|\leq 7|x-4|\)

Thus, \(\displaystyle |(x^{2}-2x-4)-4|<\epsilon\) if \(\displaystyle 7|x-4|<\epsilon\),

or if \(\displaystyle |x-4|<\frac{\epsilon}{7}\),

So, \(\displaystyle {\delta}=min(\frac{\epsilon}{7}, \;\ 1)\)

There are applets available online that can give you a graphic representation of what is going on. It is too broad a topic for me to explain it all here.
 
i restricted Snake symbol to be less than or equal to 2 not 1. then i get lost from there
 
i finally figured it out galactus . thanx so much for the help. i have been out of math for awhile and i am repeating the calc sequence again. been through all sorts of math. diffy q's, encryption, etc.


one other question if you dont mind me asking. what calculator would you recommend that would help you show step by step on how to do problems?


been thinking of getting rid of my hp.
 
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