Prove if abs|f(x)| <= B for all x#0, then lim as x->0 of xf(x) = 0,

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Homework Help Overview

The discussion revolves around proving a limit statement involving a function f(x) and its behavior as x approaches 0, specifically under the condition that the absolute value of f(x) is bounded by a constant B for all x not equal to 0.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need for a δ-ε proof and express uncertainty about how to begin the proof. There are mentions of using a given ε > 0 to determine δ, but participants are unclear on the application of this approach.

Discussion Status

Some participants are seeking guidance on how to initiate the proof, while others suggest looking at class notes or examples for direction. There is an acknowledgment of the challenge in starting the proof, but no consensus or resolution has been reached.

Contextual Notes

Participants note a reliance on traditional δ-ε proof techniques as taught by their instructor, indicating a structured approach to limit proofs is expected. There is a sense of confusion regarding the initial steps required to formulate the proof.

anthonyg
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1. if there is a number B such that abs|f(x)| <= B for all x#0, then lim as x->0 of xf(x) = 0,2. Would I be able to get some help on how to prove this?3. Given Epsilon > 0 such that delta = epsilon/B will prove the limit equals 0. (I know that may not make much sense but how am I supposed to make a solution when I don't know where to start... but I was warned so here is my attempt.) :|
 
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Welcome to PF .

It looks like a fairly direct δ-ε proof.

What have you tried?

Where are you stuck?
 
Thanks, the thing is I don't know where to start. I mean my teacher always starts out with given ε > 0 such that δ... I honestly just don't know where to go either.
 
anthonyg said:
Thanks, the thing is I don't know where to start. I mean my teacher always starts out with given ε > 0 such that δ... I honestly just don't know where to go either.
I think your teacher starts out with a given ε > 0, and then figures out what δ needs to be.

Look at your text or class notes for some examples.
 
Oh, yea, thanks! I didn't think of that!
 

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