# Precise Definition of a Limit Problem

• Sep 26th 2009, 11:24 AM
Lord Voldemort
Precise Definition of a Limit Problem
http://i132.photobucket.com/albums/q...159/ET24-4.jpg

Here's my problem. Here's what I tried:

$\displaystyle |f(x)-3| < 0.6$ whenever $\displaystyle 0 < |x-5| < \delta$
$\displaystyle |f(x)-3| < 0.6 = -0.6 < f(x)-3 < 0.6 = 2.4 < f(x) < 3.6$
The graph tells me that $\displaystyle 2.4 < f(x) < 3.6$ when $\displaystyle 4 < x < 5.7$
What I'm not completely sure about is what to do from here.
I think delta is 0.7, but I'm not sure how to conclude that mathematically.

Is this problem asking to find the smallest value of delta that the limit of f(x) at x is less then 0.6 away from 3?
• Sep 26th 2009, 11:52 AM
VonNemo19
Quote:

Originally Posted by Lord Voldemort
http://i132.photobucket.com/albums/q...159/ET24-4.jpg

Here's my problem. Here's what I tried:

$\displaystyle |f(x)-3| < 0.6$ whenever $\displaystyle 0 < |x-5| < \delta$
$\displaystyle |f(x)-3| < 0.6 = -0.6 < f(x)-3 < 0.6 = 2.4 < f(x) < 3.6$
The graph tells me that $\displaystyle 2.4 < f(x) < 3.6$ when $\displaystyle 4 < x < 5.7$
What I'm not completely sure about is what to do from here.
I think delta is 0.7, but I'm not sure how to conclude that mathematically.

Is this problem asking to find the smallest value of delta that the limit of f(x) at x is less then 0.6 away from 3?

All they want you to do here is choose one of the two lines x=4 and x=5.7 as delta. The one you choose is the one closest to x=5.

The reason being is that what you are saying is that when x is in between this line, f(x) is between the lines y=2.4 and y=3.6.

There's no math involved here. They wanted you to do this problem graphically. If they wanted you do do this analytically, they would have said so.
• Sep 26th 2009, 11:56 AM
Lord Voldemort
Cool, I think I actually understand these proofs now.
Maybe this problem wasn't so useless after all.