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July 20th, 2011, 05:22 PM   #1
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limit

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July 20th, 2011, 05:28 PM   #2
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Have you tried l'H├┤pital's rule?

Last edited by skipjack; March 2nd, 2015 at 06:13 AM.
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July 20th, 2011, 07:55 PM   #3
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Re: limit

Hello, panky!

Quote:



$\color{beige}{\text{. . . . . . . . . . . . . . . . }}$





Last edited by skipjack; March 2nd, 2015 at 06:19 AM.
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July 20th, 2011, 07:57 PM   #4
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Re: limit

We could try one-sided limits, with h > 0:

The right-hand limit is:



The left-hand limit is:



Let's now try the squeeze theorem:



Application of L'H˘pital's rule to the left-most limit, we have:

thus:



The left-hand limit is thus and the right-hand limit is . Thus, the given limit does not exist.
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July 20th, 2011, 11:02 PM   #5
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Re: limit

Thanks soroban.

Yes, MarkFL, you are right.

Thanks MarkFL.

Last edited by skipjack; March 2nd, 2015 at 06:21 AM.
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July 21st, 2011, 11:54 AM   #6
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Re: limit

Hail [color=#00BF00]MarkFL[/color], full of grace. Blessed art thou amongst moderators!

Hmm... this actually prods multiple users, for different reasons. Fun!
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July 21st, 2011, 01:26 PM   #7
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Re: limit

I don't recall anything in the Beatitudes about internet forum moderators with limited knowledge of elementary mathematics...what do I inherit?

If it's a Lamborghini, make mine a Murcielago LP 670-4 SuperVeloce with the optional 6-speed manual!! (they might be troublesome to come by as only 350 were made, so I wouldn't wait too long!)
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July 21st, 2011, 01:32 PM   #8
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Re: limit

We can dream though! One day, when I get a speedster, we'll have to tear up the coast, up 95/1/1A

And I was actually going with more of a "Hail Mary" feel, which fulfills my auxiliary function on this site as goading The Isomorphism (though accidentally).
The English translations almost always keep the flow of the Beatitudes as
"Blessed are the ______, for they/theirs _________"

At least that's what they tell me!
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July 21st, 2011, 01:41 PM   #9
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Re: limit

Yeah, I kind of figured it was a Hail Mary theme, but...I had to find a way to make it about me getting my dream car!

edit: as long as we're dreaming, have Alyssa Milano sitting in the passenger's seat when the car is delivered. Thanks.
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July 22nd, 2011, 04:11 PM   #10
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Re: limit

[color=#000000]Let me generalize it:

for a,b>0 find the limit .[/color]
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