Find the Limit as n Approaches Infinity

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    Infinity Limit
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Discussion Overview

The discussion revolves around finding the limit of the sequence defined by xn = (n^2 + log n)/(2n^3 - 1)^(1/2) as n approaches infinity. Participants explore the mathematical steps involved in simplifying the expression and determining the limit, focusing on the behavior of the numerator and denominator.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant suggests taking out n^2 from the numerator and denominator, leading to confusion about obtaining a 0 in the denominator.
  • Another participant corrects this by stating that the 1 should also be divided by n^2, implying that the denominator does not approach 0.
  • Further contributions clarify the expression for the denominator after dividing by n^2, with one participant correcting their earlier statement about the terms involved.
  • There is a proposal to consider the limits of the numerator and denominator separately as n approaches infinity.
  • Another participant suggests rationalizing the denominator as a potential method to simplify the limit calculation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to finding the limit, and multiple viewpoints regarding the simplification steps and the behavior of the expression remain present.

Contextual Notes

Participants express uncertainty regarding the correct manipulation of the expression and the implications of their simplifications. There are unresolved mathematical steps related to the limit calculation.

Mattofix
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Please help, i take out n^2 top and bottom so end up with 0 as demominator...

Find lim (n to infinity) xn

xn = (n^2 + log n)/(2n^3 - 1)^(1/2)


...?
 
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You won't get a 0 in the denominator. You forgot to divide the 1 by n^2.
 
if i divide the bottom by n^2 i get (1/n + 1/n^4)
 
sorry... (1/n - 1/n^4)^(1/2)
 
damn, sorry again, i mean (2/n - 1/n^4)^(1/2)
 
which becomes 0 as n tends to infinity?
 
[tex]\lim_{n\to \infty} x_n = \lim_{n\to\infty} \left( \frac{ 1+ \frac{\log n}{n^2} }{ \sqrt{ \frac{2n^3-1}{n^4}}} \right)[/tex]

Consider separately, what is the numerator tending towards? How about the denominator?
 
Last edited:
Rationalize the denominator

Try rationalizing the denominator first. Then things get much easier.
 

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