Evaluate this limit, introductory real analysis

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Homework Help Overview

The discussion revolves around evaluating the limit of a sequence defined by the expression \((-3n^2+n+1)/(n^2-2n+3\)). This falls under the subject area of introductory real analysis, specifically focusing on limits of sequences.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss various methods for evaluating the limit, including the definition of a limit and the squeeze theorem. There are attempts to manipulate the expression for simplification, with some participants questioning the validity of their approaches and the need for factoring.

Discussion Status

The discussion is active, with participants sharing different strategies and clarifying misunderstandings about the methods suggested. Some guidance has been offered regarding factoring and the application of the squeeze theorem, indicating a productive exploration of the problem.

Contextual Notes

Participants mention constraints related to the use of certain methods, such as l'Hospital's rule, and express uncertainty about the implications of dividing by terms in the expression.

jaqueh
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Homework Statement


limit of the sequence, [xn]=(-3n2+n+1)/(n2-2n+3)


Homework Equations


I so far know about the definition of a limit, squeeze principle, and lim[xnyn] = 0 if xn or yn goes to 0


The Attempt at a Solution


Tried the definition of the limit but the algebra got really crazy so i don't think I'm supposed to do it that way. I'm trying to squeeze it between (-3n2/n2) and (-3n3)/(n3), but i don't know if i can prove that the cubed one is greater than my sequence
 
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Try factoring out a variable of the highest power. This is a standard method for problems like these before l'Hospital's rule is introduced.

Edit: Just in case you aren't allowed to use that method..

If you want to use the squeeze theorem and then the definition of the limit, you need to factor out some terms by manipulating the original expression so they cancel out.
 
Last edited:
ah I've divided the numerator by 3 but am still stuck. I know it hits -3.

yeah I'm trying to see what I can make the expression into so things will start cancellong
 
Did you misunderstand what scurty said? Nothing about dividing by -3: factor out, or, same thing, divide both numerator and denominator by n^2.
 
ok great I have it now. I do that then squeeze because I'm not allowed to say yet that 1/n goes to zero in a sequence I think
 

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