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

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The limit of 5/(x^2 - 4) as x approaches 2 from the right is positive infinity. As x gets closer to 2, the denominator x^2 - 4 approaches 0 while remaining positive, resulting in an unbounded increase in the function's value. A table of values shows that f(x) increases significantly as x nears 2 from the right. There is a consensus that looking up answers is unproductive, with some participants expressing frustration over this approach. The discussion also touches on the banning of a user, adding a social dynamic to the mathematical topic.
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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.
 
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