Is Finding a Common Denominator Necessary for Evaluating This Limit?

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Discussion Overview

The discussion revolves around evaluating a limit involving trigonometric functions as \( x \) approaches 0. Participants explore whether finding a common denominator is necessary for this evaluation, with a focus on the behavior of the limit and the mathematical expressions involved.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about how to evaluate the limit, specifically \( \lim_{x\rightarrow0} \left(\frac{1}{\sin 2x} + \frac{1}{x^2}\right) \).
  • Another participant suggests that the limit may go to infinity, referencing a simpler limit \( \lim_{x\to 0^+} \frac{1}{x} \) as a related example.
  • A participant questions whether the limit might involve subtraction instead, proposing \( \lim_{x\to 0}\left(\frac{1}{\sin^2x} - \frac{1}{x^2}\right) \) as a potential alternative.
  • One participant, who has not taken calculus, asks if finding a common denominator is necessary for the evaluation.
  • Another participant, also without calculus experience, responds that a common denominator is not needed in this case, citing that both parts of the expression are positive and tend to infinity as \( x \to 0 \).

Areas of Agreement / Disagreement

Participants express differing views on whether a common denominator is necessary, with some suggesting it is not needed while others raise questions about the limit's evaluation. The discussion remains unresolved regarding the necessity of a common denominator and the correct formulation of the limit.

Contextual Notes

There are limitations in the discussion, including the lack of calculus knowledge among some participants and the potential ambiguity in the original limit expression. The mathematical steps and assumptions involved in evaluating the limit are not fully explored.

Lizwi
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How do I evaluate this limit I have no Idea, I'm sorry for not showing my work please!

limx[itex]\rightarrow[/itex]0 [itex]\frac{1}{sin<sup>2</sup>x}[/itex] +[itex]\frac{1}{x<sup>2</sup>}[/itex]
 
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Doesn't it go to infinity?
 


What happens when you have...

[itex]lim_{x\to 0^+} \frac {1}{x}[/itex]

That is a basic limit, answering that should lead you to what you want.
 


When using itex, you wouldn't use the other tags that the board uses such as for superscripts; you would use ^ to make exponents.

Could you have meant this limit with subtraction instead?
[itex]\lim_{x\to 0}\frac{1}{\sin^2x} - \frac{1}{x^2}[/itex]
 
Last edited:


Lizwi said:
How do I evaluate this limit I have no Idea, I'm sorry for not showing my work please!

[tex]\lim_{x\to 0}\left(\frac{1}{sin^2x}+\frac{1}{x^2}\right)[/tex]


I already edited your post above. Now read the other posts.

DonAntonio
 


I have not taken calc yet, but would he need to find a common denominator?
 


ME_student said:
I have not taken calc yet, but would he need to find a common denominator?


Kudos for the courage to post without having yet studied calculus..:) In this case it isn't needed to find

common denominator as: (1) both parts of the expression are positive, (2) it's a sum and (3) both tend to [itex]\infty[/itex] as [itex]x\to 0[/itex]

DonAntonio
 

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