What Is the Limit of n*sin(1/n^2) as n Approaches Infinity?

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Discussion Overview

The discussion revolves around finding the limit of the expression n*sin(1/n^2) as n approaches infinity, along with another limit involving a square root expression. The scope includes mathematical reasoning and limit evaluation.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant seeks help with two limit problems, indicating confusion about the concepts involved.
  • Another participant points out issues with special symbols in the original post, suggesting a need for clearer notation.
  • A later reply reformulates the limit questions for clarity, specifically asking for the limit of n*sin(1/n^2) and another expression involving a square root.
  • One participant suggests a method for evaluating the first limit by manipulating the square root and proposes a substitution for the second limit involving n.

Areas of Agreement / Disagreement

The discussion remains unresolved, with no consensus on the limits or methods to evaluate them. Participants express different levels of understanding and approaches to the problems.

Contextual Notes

Some assumptions about the notation and mathematical steps may be unclear, and there is a dependence on the correct interpretation of the expressions presented.

dickshant
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Hello, can anyone help me with these questions... At least one of them please... thank you

1 Find the limit as → ∞, if it exists, of:(i) √︀( ( + 1)) − 2 , (ii) sin(1/(^2))
I really cannot understand how to do this.:confused:..thanks for your help:):)
 
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You seem to be using a number of "special symbols". All my viewer shows is a square for each.
 


ok...i will reformulate the question
find the limit as n tends to infinity, if it exists of
1. root(n(n+1))-2n

2. n*sin(1/n^2)
Thanks...:)
 


For the first one, multiply out what you have in the square root and pull out n2 from the square root.
For the second, you might try the substitution u = 1/n
 

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