Proving a Limit: Epsilon & Delta Solution

Thread starter ace123
Start date Sep 15, 2007
Tags

Limit

Click For Summary

The discussion focuses on proving the limit of a rational function using the epsilon-delta definition. Participants clarify how to handle the numerator and denominator after factoring out (x-5) and emphasize the importance of bounding the fraction formed by these expressions. They suggest restricting x to a specific interval to ensure the denominator does not approach zero and to find maximum and minimum values for bounding. The conversation culminates in establishing that for a chosen delta, the limit can be shown to be -3 by demonstrating that the function's deviation from the limit can be made less than epsilon. The participants express gratitude for the collaborative problem-solving approach that enhances understanding of epsilon-delta proofs.

Sep 15, 2007

ace123

learningphysics said:

|(x^2+2x+1)/(x^2-8x+14)| is bounded above by 42.25/1.75 over the range of |x-5|<1/2. If we didn't know that |x-5|<1/2, we wouldn't be able to use this bound.

Thanks. you're welcome. I really appreciate the compliment. But don't take my word for anything, or anyone else... convince yourself... it's possible I made a mistake. anyway, good luck on your exam!

Oh I understand now. I guess i completely forgot that we had to restrict x to the 1/2 interval. It makes complete sense now. I really appreciate you help and thanks