Dominant Terms in Calculus Limits

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Discussion Overview

The discussion revolves around identifying the dominant terms in a limit expression involving polynomial, exponential, logarithmic, and square root functions as x approaches infinity. Participants are attempting to determine both the dominant terms in the numerator and denominator and the overall limit of the expression.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that the dominant term in the numerator is \(x^7\), but expresses uncertainty due to conflicting information from their assignment.
  • Another participant references a document that claims the dominant term in the numerator is the exponential term, indicating a potential correction to the first participant's assertion.
  • In the denominator, one participant argues that \(\sqrt{10x-1}\) should be the dominant term based on the same document.
  • There is a claim that the limit approaches infinity, but this is contested by another participant who states that the limit is actually \(-\infty\).
  • Multiple participants express confusion regarding the correctness of their interpretations and the assignment's claims.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the dominant terms or the limit. There are competing views on which terms are dominant and what the limit evaluates to, indicating an unresolved discussion.

Contextual Notes

Participants reference an assignment that contradicts their interpretations, leading to uncertainty about the correct dominant terms. The discussion also highlights differing interpretations of dominance in the context of limits.

spingo
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Hello, I am having issues finding the dominant terms in the following expression:

lim [(x^7)-9(e^x)] / [sqrt(10x-1)+8*ln(x)]
x->infinity

Prompt: Find the limit and the dominant term in the numerator and denominator.
 
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Link to a decent explanation of dominance ...

Dominance
 
So the dominant term in the numerator is should be (x^7)? According to my assignment this is incorrect but I'm not sure how. Additionally, by the logic used in the document sqrt(10x-1) should be dominant in the denominator.

The limit should be infinity then?

My assignment claims all of these answers are incorrect.
 
spingo said:
So the dominant term in the numerator is should be (x^7)? According to my assignment this is incorrect but I'm not sure how. Additionally, by the logic used in the document sqrt(10x-1) should be dominant in the denominator.

The limit should be infinity then?

My assignment claims all of these answers are incorrect.

dominant term in the numerator is the exponential, as stated clearly in the link.

yes, dominant term in the denominator is the square root function

the limit is $-\infty$
 

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