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**zetafunc.****Guest**

zetafunc. wrote:

It is definitely incorrect.

Whoops, I meant

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,658

Hi;

That is close but not correct.

**In mathematics, you don't understand things. You just get used to them.**

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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: 90,658

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.**

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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: 90,658

Which textbook?

**In mathematics, you don't understand things. You just get used to them.**

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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: 90,658

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

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

Just below the question.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,658

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

I do not think 2 / 3 is correct.

**In mathematics, you don't understand things. You just get used to them.**

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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: 90,658

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

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

What are you getting?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,658

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

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

So this could be one of those bogus questions?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,658

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.

**In mathematics, you don't understand things. You just get used to them.**

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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: 90,658

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.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

The EbenezerSon guy?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,658

Yes, his textbook is a mess.

**In mathematics, you don't understand things. You just get used to them.**

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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: 90,658

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

**In mathematics, you don't understand things. You just get used to them.**

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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: 90,658

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.

**In mathematics, you don't understand things. You just get used to them.**

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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?