Limit of 1/x as x Approaches 0: Infinity?

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Discussion Overview

The discussion centers on the limit of the function 1/x as x approaches 0, exploring whether it can be considered infinity or if the limit does not exist. The scope includes mathematical reasoning and conceptual clarification regarding limits and asymptotic behavior.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether the limit of 1/x as x approaches 0 is infinity.
  • Another participant asserts that the limit does not exist.
  • A later reply supports the claim that the limit does not exist, explaining that the left limit approaches negative infinity while the right limit approaches positive infinity, indicating a vertical asymptote at y = 0.
  • One participant suggests that a sign chart could be used to prove the behavior of the function 1/x around x = 0.

Areas of Agreement / Disagreement

Participants express disagreement regarding the limit's existence, with some asserting it does not exist and others suggesting it approaches infinity.

Contextual Notes

The discussion highlights the importance of left and right limits in determining the behavior of the function near the point of interest, as well as the implications of vertical asymptotes.

calvinnn
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What is the limit of 1/x as x approaches 0. Is it infinity?
 
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The limit does not exist.
 
k thanks a lot
 
Tide said:
The limit does not exist.


Well, that is correct because the left-limit is not equal to the right limit. In deed the function y = 0 is the vertical asypmtote of this given function. The left limit is the negative infinity and the right limit is the positive infinity. One can prove this by making a sign chart of the function 1/X


regards
marlon
 

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