another calc question...regarding the evil epsilon and delta...

[mAdD INDIAN]

Ok..say you have the following:

Prove lim x-->a f(x)/g(x) = L/M

how would you go about it if you know you can't factor out hte f(x) and g(x) to get it on one line wihtout a numerator and denominator.

I know you have to break it down and do it individually..but I can't figure out how to connect it together.

and if you wanna know wat the actual question is..its

lim x-->2 (x^3 - 4x + 5)/(x^2 - 2x +1) = 5/7

however right now i am trying to prove e-d for hte general case of f(x)/g(x) so i understand it before i tackle the problem. I did prove the case of f(x) + g(x) = L + M using E-D...however this one seems to be difficult!

DAMN YOU EPSILON AND DELTA!

 

[mAdD INDIAN]

bump!

i really need to know this guys..i've been trying to figure it out for a few days now!

 

[mAdD INDIAN]

ok I think I got it..not sure though.

Is it min = { 1, 2E/3} ; E = epsilon

heres what i did...i simplified it so it equals

(x^2 + 2x | x + 2|)/(x^2 - 2x + 1) < E

then I let (x^2 + 2x / x^2 - 2x + 1) = k --- eq1

now I assume D (delta) = 1.

so: |x -2| < 1 ==> -1 < |x-2| < 1 ==> 1 < x < 3

now here's the part im confused about...do you let x=3 or x = 1? ..anyway i let x = 1 for simplicity

sub x=1 in eq1 to get k = 3/2

so then 3/2|x-2| < E ==> |x-2| < 2/3E

therefore 2/3E = D

is that correct?

 

[kherman]

Originally posted by: mAdD INDIAN
Ok..say you have the following:

Prove lim x-->a f(x)/g(x) = L/M

how would you go about it if you know you can't factor out hte f(x) and g(x) to get it on one line wihtout a numerator and denominator.

I know you have to break it down and do it individually..but I can't figure out how to connect it together.

and if you wanna know wat the actual question is..its

lim x-->2 (x^3 - 4x + 5)/(x^2 - 2x +1) = 5/7

however right now i am trying to prove e-d for hte general case of f(x)/g(x) so i understand it before i tackle the problem. I did prove the case of f(x) + g(x) = L + M using E-D...however this one seems to be difficult!

DAMN YOU EPSILON AND DELTA!

lim->2 ??

Sure it's not lim -> inifintiy of
(2*(x^3-4x+5)/(x^2-2x+1)

The lim->2 makes no sense??? It's easy to solve.