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**zetafunc.****Guest**

zetafunc. wrote:

It is definitely incorrect.

Whoops, I meant

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Hi;

That is close but not correct.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

Yes, it is because I used [0, π/2] as the interval instead of [0, π/4]. The only reason for the high accuracy (16 decimal places) is because the area in the interval [π/4, π/2] is so small.

Nevertheless it seems a good enough approximation for Agnishom's purposes as he rounded his answer to 14 d.p.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Yes, the graph shows it dives down pretty hard to the x axis so that the tail is very, very tiny. Agnishom got his answer using Maxima.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

I think I can get an exact answer using the same way I got that one -- with a beta function trick or maybe even a contour (an eighth of a circle). I will work on it later.

Can you help me evaluate this limit?

The textbook has it listed under a L'Hopital's rule exercise, and they give the answer as 2/3. Problem is, I do not see how to apply it here -- from the looks of it, if I keep on differentiating I'll just get another trig function which cannot be evaluated at infinity (it'd be indeterminate).

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Which textbook?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

Schaum's Outlines, Advanced Calculus, by Spiegel. Page 95, Q4.75(k).

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Yes, I am looking at that one. Where does he say 2 / 3 is the answer?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Just below the question.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Sorry, I had to upgrade my version. On mine he left out the answers.

I do not think 2 / 3 is correct.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

What answer are you getting, and how did you do it?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

I tried to work it numerically to check and I keep getting something that is negative!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

What are you getting?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Mathematica gets numerically -0.814882463329968. I do not think that is correct because this might have an interval for an answer.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

So this could be one of those bogus questions?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Yes, it is a clear typo. Try taking the limit as x approaches 0. That will help greatly.

The problem should be:

that equals 2 / 3.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Thanks for pointing that out -- I am getting that answer now, too.

This textbook is really annoying me. There are a ridiculous number of typos, probably several in at least every exercise. The questions are nice but unfortunately part of the challenge appears to be working out what the hell he meant to write in the first place.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Yes, that is true. There is a guy who comes in here whose is trying to teach himself some math. Unfortunately, his textbook is a total piece of garbage. Typos in both questions and answers, overly complicated problems and it is confusing him.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

The EbenezerSon guy?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Yes, his textbook is a mess.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

I think sometimes it is best to have two textbooks for a particular subject. One that just guides you on how to solve the problems in a clear and concise manner, and another that gives a more rigorous treatment of the subject.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

I would settle for the first one every time but most of the time you are lucky to get either.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

The more specialised the topic is the harder it is to get a decent treatment of the subject.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

I agree, although a while back I went through all the books at the University library on DE's as a test. I found many duplicated pages and problems that were word for word. It appeared to me that these 150 authors all read one gigantic book and wrote 150 smaller ones.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Hmm, that is interesting. Of course there are always going to be identical questions here and there -- but it does raise an interesting question. Can you copyright a maths question? Or is it only the answerer that is bickered over?