What is the limit of F(X) = 0/X as X approaches zero?

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Discussion Overview

The discussion centers on finding the limit of the function F(X) = 0/X as X approaches zero. Participants explore various methods of determining this limit, including algebraic approaches and references to l'Hôpital's rule.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that the limit is 0 for all values of X not equal to zero, viewing F(X) as a constant function.
  • Others suggest using l'Hôpital's rule to arrive at the same conclusion of the limit being 0.
  • One participant expresses a desire to find the limit using algebra rather than l'Hôpital's rule.
  • Another participant proposes an algebraic manipulation of 0/X to illustrate that the limit approaches 0.
  • A participant mentions that the limit is undefined at X = 0 but approaches 0 as X approaches 0.
  • Some participants discuss the concept of limits in the context of sequences, questioning how 0/X behaves as X approaches 0 through a sequence.
  • There is a challenge regarding the complexity of certain solutions, with some arguing that simpler explanations are preferable.

Areas of Agreement / Disagreement

While several participants agree that the limit approaches 0, there are differing views on the methods to demonstrate this and some uncertainty about the definitions and concepts of limits, particularly in relation to sequences.

Contextual Notes

Some participants express confusion regarding the definition of limits and the application of sequence limits, indicating potential gaps in understanding that are not fully resolved in the discussion.

Who May Find This Useful

This discussion may be useful for students or individuals interested in calculus, particularly those exploring limits and different methods of evaluating them.

racer
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Hey there

Find the lim of F(X) as X approaches zero

F(X) = 0/X ( Zero over X )

Thanks.
 
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Well its a constant function equal to 0 for all values of x not equal to zero. So we can see the limit is equal to 0.
 
You could also use l'Hopital and get the same answer as Gib_Z provided.
 
Well its a constant function equal to 0 for all values of x not equal to zero. So we can see the limit is equal to 0.

You could also use l'Hopital and get the same answer as Gib_Z provided.

Yeah it is zero but I want the lim without L'Hopital rule, I want the solution using Algebra.
 
Find the Lim of 0/X as X approaches zero.

0/X = X-X/X = X/X - X/X = 1-1 = 0
 
alternatively you can say that if y is a member of the the Reals then 0*y=0 set y=1/x. While not wrong, your solution simply overcomplicates things.
 
no matter what x is, the answer will always be 0. unless x = 0, then it is undefined. so you can say it is just approaching 0
 
f(x) approaches L as x goes to a if and only if f(x_n) approaches L for any sequence of numbers x_n approaching a.

Let x_n be any sequence of numbers approaching 0. What is 0/x_n? What is the limit of that sequence.
 
f(x) approaches L as x goes to a if and only if f(x_n) approaches L for any sequence of numbers x_n approaching a.

Let x_n be any sequence of numbers approaching 0. What is 0/x_n? What is the limit of that sequence.

I don't know anything about Sequence limits.
 
  • #10
But you ask of the limit of continuous functions?
 
  • #11
Do you know the definition of a limit? If so it is obviously zero.
 

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