Is the Limit of 5/(x^2 - 4) as x Approaches 2 from the Right Positive Infinity?

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Discussion Overview

The discussion centers around the limit of the function 5/(x^2 - 4) as x approaches 2 from the right. Participants explore the behavior of the function near this point, considering both numerical examples and theoretical reasoning.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents a table of values showing that as x approaches 2 from the right, the function values increase significantly, suggesting the limit is positive infinity.
  • Another participant supports this by noting that for x close to 2 and positive, the denominator approaches 0 and remains positive, while the numerator is positive, leading to the conclusion that the limit is positive infinity.
  • Several posts express frustration with looking up answers instead of engaging with the problem, indicating a preference for discussion over simply finding solutions.

Areas of Agreement / Disagreement

Participants generally agree on the interpretation of the limit approaching positive infinity, but there is a notable disagreement regarding the value of looking up answers versus engaging in the discussion.

Contextual Notes

Some assumptions about the behavior of the function near the limit point are present, but there are no explicit mathematical steps provided to support the claims made.

Who May Find This Useful

Readers interested in limit calculations, particularly in the context of calculus, may find this discussion relevant.

nycmathdad
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Find the limit of 5/(x^2 - 4) as x tends to 2 from the right side.

Approaching 2 from the right means that the values of x must be slightly larger than 2.

I created a table for x and f(x).

x...2.1...2.01...2.001
f(x)...12...124.68...1249.68

I can see that f(x) is getting larger and larger and possibly without bound.

I say the limit is positive infinity.

Yes?
 
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Problem 1.5.29.
Odd numbered.
Look up the answer.
 
For x close to 2 and positive, the denominator, x^2- 4, is close to 0 and positive while the numerator, 5, is positive. That is enough to say that the limit, as x goes to 2 from the right, is positive infinity.
 
jonah said:
Problem 1.5.29.
Odd numbered.
Look up the answer.
Well that's no fun!
 
Country Boy said:
Well that's no fun!

Exactly. Looking up the answer is for idiots, for lazy pieces of you know what.
 
Beer soaked ramblings follow.
nycmathdad said:
Country Boy said:
Well that's no fun!
Exactly. Looking up the answer is for idiots, for lazy pieces of you know what.
Translation: I like it when someone is on my side for a change as opposed to the usual criticism I get. It emboldens me to call people names.

P.S. I just noticed that nycmathdad just got banned again.
 
Last edited:

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