Limits of 1/x Explained: A Calculus Question

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    Calculus Limits
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Discussion Overview

The discussion revolves around the limit of the function 1/x as x approaches 0 from the positive side. It explores the application of the Squeeze theorem in this context and addresses a misunderstanding related to the inequalities involved.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • A participant inquires about the limit of 1/x as x approaches 0 from the positive side, noting that the graph suggests the limit is +Infinity.
  • The same participant attempts to apply the Squeeze theorem, proposing that 1/(x+1) < 1/x < 1 for small positive x, and concludes that the limit should be 1.
  • Another participant points out an error in the initial claim that 1/x < 1 for small positive x.
  • The first participant acknowledges the mistake and expresses gratitude for the correction.
  • A later reply encourages the first participant not to be discouraged by the mistake.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the application of the Squeeze theorem in this case, as there is a clear disagreement regarding the inequalities used in the argument.

Contextual Notes

The discussion highlights a misunderstanding related to the behavior of the function 1/x near zero and the conditions under which the Squeeze theorem can be applied. The specific inequalities proposed by the first participant are not valid for the limit in question.

Samit Chak
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This may be a very basic question for this forum. I have just started to Learn Calculus. Please. help me with my question -
Suppose I need to find the Limit of 1/x where x tends to 0 from positive side.
I know from the graph of 1/x that answer is +Infinity.
But if I apply Squeeze theorem to it and the greater function is 1 and smaller function is 1/(1+x).
1/(x+1) < 1/x < 1 : where x is always positive and tends to 0.
The limits of these rightmost and leftmost functions at 0+ is 1. So as per squeeze th. the middle function is 1.

Why it is different from the actual answer? Am I doing something wrong?
 
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Yes. You have erroneously stated that 1/x < 1 for small positive x
 
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Likes   Reactions: Samit Chak
oh...such a bad mistake...
thanks David for replying and pointing it out...
 
no problem. don't let it discourage you!
 

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