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You are not logged in. #11801 20130724 04:43:40
Re: Linear Interpolation FP1 Formula
Whoops, I meant #11802 20130724 04:46:57
Re: Linear Interpolation FP1 FormulaHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11803 20130724 04:49:24
Re: Linear Interpolation FP1 FormulaYes, 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. #11804 20130724 04:55:23
Re: Linear Interpolation FP1 FormulaYes, 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. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11805 20130724 04:59:40
Re: Linear Interpolation FP1 FormulaI 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. 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 20130724 05:02:42
Re: Linear Interpolation FP1 FormulaWhich textbook? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11807 20130724 05:21:56
Re: Linear Interpolation FP1 FormulaSchaum's Outlines, Advanced Calculus, by Spiegel. Page 95, Q4.75(k). #11808 20130724 05:27:10
Re: Linear Interpolation FP1 FormulaYes, 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. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11809 20130724 05:39:37#11810 20130724 05:45:32
Re: Linear Interpolation FP1 FormulaSorry, I had to upgrade my version. On mine he left out the answers. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11811 20130724 06:01:15
Re: Linear Interpolation FP1 FormulaWhat answer are you getting, and how did you do it? #11812 20130724 06:11:06
Re: Linear Interpolation FP1 FormulaI 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. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11813 20130724 06:16:39#11814 20130724 06:23:45
Re: Linear Interpolation FP1 FormulaMathematica 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. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11815 20130724 06:26:37
Re: Linear Interpolation FP1 FormulaSo this could be one of those bogus questions? #11816 20130724 06:31:43
Re: Linear Interpolation FP1 FormulaYes, it is a clear typo. Try taking the limit as x approaches 0. That will help greatly. that equals 2 / 3. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11817 20130724 07:44:28
Re: Linear Interpolation FP1 FormulaThanks for pointing that out  I am getting that answer now, too. #11818 20130724 10:58:01
Re: Linear Interpolation FP1 FormulaYes, 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. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11819 20130724 20:22:37#11820 20130724 20:29:21
Re: Linear Interpolation FP1 FormulaYes, his textbook is a mess. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11821 20130724 20:49:07
Re: Linear Interpolation FP1 FormulaI 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 20130724 20:54:25
Re: Linear Interpolation FP1 FormulaI 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. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11823 20130724 22:21:00
Re: Linear Interpolation FP1 FormulaThe more specialised the topic is the harder it is to get a decent treatment of the subject. #11824 20130724 22:28:01
Re: Linear Interpolation FP1 FormulaI 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. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11825 20130725 19:15:55
Re: Linear Interpolation FP1 FormulaHmm, 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? 