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#11801 2013-07-23 06:43:40

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

zetafunc. wrote:

It is definitely incorrect.

Whoops, I meant

#11802 2013-07-23 06:46:57

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

Re: Linear Interpolation FP1 Formula

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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#11803 2013-07-23 06:49:24

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

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.

#11804 2013-07-23 06:55:23

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

Re: Linear Interpolation FP1 Formula

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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#11805 2013-07-23 06:59:40

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

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).

#11806 2013-07-23 07:02:42

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

Re: Linear Interpolation FP1 Formula

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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#11807 2013-07-23 07:21:56

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

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

#11808 2013-07-23 07:27:10

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

Re: Linear Interpolation FP1 Formula

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11809 2013-07-23 07:39:37

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Just below the question.

#11810 2013-07-23 07:45:32

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

Re: Linear Interpolation FP1 Formula

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11811 2013-07-23 08:01:15

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

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

#11812 2013-07-23 08:11:06

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

Re: Linear Interpolation FP1 Formula

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11813 2013-07-23 08:16:39

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

What are you getting?

#11814 2013-07-23 08:23:45

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

Re: Linear Interpolation FP1 Formula

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11815 2013-07-23 08:26:37

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

So this could be one of those bogus questions?

#11816 2013-07-23 08:31:43

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

Re: Linear Interpolation FP1 Formula

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11817 2013-07-23 09:44:28

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

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.

#11818 2013-07-23 12:58:01

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

Re: Linear Interpolation FP1 Formula

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11819 2013-07-23 22:22:37

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

The EbenezerSon guy?

#11820 2013-07-23 22:29:21

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

Re: Linear Interpolation FP1 Formula

Yes, his textbook is a mess.


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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#11821 2013-07-23 22:49:07

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

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.

#11822 2013-07-23 22:54:25

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

Re: Linear Interpolation FP1 Formula

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11823 2013-07-24 00:21:00

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

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

#11824 2013-07-24 00:28:01

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

Re: Linear Interpolation FP1 Formula

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#11825 2013-07-24 21:15:55

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

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?

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