Find Tolerance Limit for f(x)=x^2.5 Near 0

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Homework Help Overview

The discussion revolves around finding the tolerance limit for the function f(x) = x^2.5 as x approaches 0 from the positive side. Participants are examining how close the input must be to 0 to ensure the output remains within 0.1 of the limit, which is 0.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the relationship between the input values and the corresponding outputs of the function near the limit. There are questions regarding the correctness of the computed outputs for specific inputs and the implications of those outputs in relation to the limit.

Discussion Status

Some participants have attempted calculations to determine the appropriate input values that keep the output within the specified range. There is an acknowledgment of potential errors in reasoning, and further clarification is being sought on the approach to solving the problem.

Contextual Notes

Participants are working under the constraint that the output must remain within 0.1 of the limit as x approaches 0. There is an ongoing examination of the assumptions related to the function's behavior near this point.

mnzavislan
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Homework Statement



Consider f(x)=x^2.5. Note that limf(x) as x->0+ =0. The input must be less than ___ from 0 to guarantee the output is within 0.1 of the limit.

Homework Equations



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The Attempt at a Solution

 
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If I'm correct, the output can be 0.1 and -0.1. So I have computed:
f(0.1)= 0.00316 and f(-0.1)= -0.00316
These are the inputs that guarantee the output to be within 0.1 of the limit, 0. However, I think there is an error in my thinking somewhere.
 
You used 0.1 as an input.

Solve f(x-0) = 0 + 0.1 for x.
 
Ohhh okay! Got it. Thank you so much.
 

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