Need some help with understanding linear approximations

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Discussion Overview

The discussion revolves around understanding linear approximations in mathematics, particularly in the context of calculating approximate values for functions. Participants are exploring the concept, its application, and specific calculations related to the function f(x) = x^4, aiming to approximate (2.94)^4.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in understanding linear approximation and requests help with a specific calculation involving (2.94)^4.
  • Another suggests using x = 3 and Δx = -0.06 to approximate the value.
  • Several participants discuss the derivative of the function f(x) = x^4 and its relevance to the approximation.
  • There are various attempts to calculate the approximation, with some participants providing their calculations and questioning their results.
  • Some participants emphasize the importance of choosing a whole number close to the target value for easier calculations.
  • One participant critiques the book's explanation of the topic, indicating confusion and frustration with the material.
  • Another participant explains that the approximation improves with smaller values of Δx relative to x.
  • There is a discussion about the binomial expansion and its relation to linear approximation, with differing opinions on its appropriateness for the task at hand.

Areas of Agreement / Disagreement

Participants generally agree on the method of using linear approximation but express different views on the calculations and the clarity of the book's explanations. There is no consensus on the specific calculations or the best approach to take.

Contextual Notes

Some participants mention the need for clarity on the choice of Δx and the implications of using different values for x. There are unresolved questions about the accuracy of the approximations and the steps involved in the calculations.

  • #31
LCKurtz said:
Apparently you've got it now, but I would suggest part of your problem is inability to do algebra/arithmetic.
As epenguin said "we all have our blind moments".
 

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