Find the Limits: Testing the Boundaries

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    Limits Testing
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Discussion Overview

The discussion revolves around evaluating limits in calculus, specifically focusing on two limit problems presented by a participant. The scope includes mathematical reasoning and the interpretation of limits, particularly in cases where the limits may be undefined or approach infinity.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents two limit problems and expresses uncertainty about the correctness of their answers.
  • Another participant suggests that understanding the behavior of the function is crucial for determining the limit.
  • Some participants argue that the second limit is undefined, while others propose different values such as -5 and -infinity.
  • A participant questions the interpretation of limits, emphasizing that the goal is to find the value a function approaches rather than simply stating it is undefined.
  • There is a distinction made between limits that approach infinity and those that are undefined, with some participants asserting that stating a limit is undefined is a factual statement rather than a complaint.

Areas of Agreement / Disagreement

Participants express disagreement regarding the values of the second limit, with multiple competing views on whether it approaches -5, -infinity, or is undefined. The discussion remains unresolved as no consensus is reached on the correct interpretation of the limits.

Contextual Notes

Participants reference the behavior of functions near points of interest, but there are unresolved assumptions regarding the definitions and conditions under which limits are evaluated. The discussion also highlights potential confusion surrounding the classification of limits as defined or undefined.

PistonsMVP
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Find the Limits1. lim 312
x->11+

2. lim (x^2 +9)/(x^2 -1)
x->1for #2 i got 10 as the answer, but I'm not sure if its right. Thanks

edit: Sorry, wrong forum
 
Last edited:
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1) do you know what a limit is? if so, looking at the behavior of the function should hint you as to what the answer is.

2) 10 isn't the correct answer. many people confuse the answers of 0/0 and x/0 or 0/x. The former gives odd results, whereas the latter two produce the same result, no matter what x is.
 
phreak what do you mean by "the former gives odd results?"PistonsMVP, the limit of a contant function is what?
 
nm i figured it out. #1 is 312
and #2 DNE because 10/0
 
excuse me...isnt the point of a limit to find what value it approaches and not complain that its undefined?

btw the 2nd limit is -infinity
 
Last edited:
Gib Z said:
excuse me...isnt the point of a limit to find what value it approaches and not complain that its undefined?

o btw the 2nd limit is -5

How is it -5?
 
d_leet said:
How is it -5?

It is not -5. And there is a big difference between 10/0, which is undefined, and the limit of the function as x -> 1.
 
Gib Z said:
excuse me...isnt the point of a limit to find what value it approaches and not complain that its undefined?

btw the 2nd limit is -infinity
Saying that the limit is -infinity is just a way of saying that it is not defined. Saying that a limit is undefine is not "complaining", it is stating a fact.
 
[tex]\lim_{x \to a} f(x) = +\infty[/tex] or [tex]\lim_{x \to a} f(x) = -\infty[/tex]

Just describes HOW a limit is not defined (whether it can be made arbitrarily large positive/large negative as x->a), but it definitely is not defined!
 

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