NSX Posted June 14, 2003 Share Posted June 14, 2003 Just a little food for thought kinda thread here; what ways are there to find the numerical value of "e", that is, the natural base. There's 2 I learned this semester: 1. 1/1! + 2/2! + 3/3! + ... n/n!, as n-->infinity where n is an element of natural numbers Or something like that and 2. The fundamental limit of calculus, that is: lim x-->infinity for (1 + 1/x)^x Link to comment Share on other sites More sharing options...
JaKiri Posted June 14, 2003 Share Posted June 14, 2003 It's e = 1/0! + 1/1! + 1/2! + 1/3! (etc), which is something called a Taylor series; you get a good value out pretty quickly too. Link to comment Share on other sites More sharing options...
NSX Posted June 14, 2003 Author Share Posted June 14, 2003 Originally posted by MrL_JaKiri It's e = 1/0! + 1/1! + 1/2! + 1/3! (etc), which is something called a Taylor series; you get a good value out pretty quickly too. Yeah; something like that...lol That's the taylor series eh? I see; I hear you math gurus talking about it alot; where else do you use this taylor series? Link to comment Share on other sites More sharing options...
JaKiri Posted June 14, 2003 Share Posted June 14, 2003 A taylor series assumes you can express a function as an infinite sum of the differations of the function, basically. Link to comment Share on other sites More sharing options...
Dave Posted June 14, 2003 Share Posted June 14, 2003 It's very useful for proving things like Euler's formula (e^(pi * i) +1 = 0) and stuff like that. Not sure I can think of anything else to use it for, but it's mainly used in proofs and such things. And approximations to things like circular/hyperbolic functions etc. Link to comment Share on other sites More sharing options...
NSX Posted June 14, 2003 Author Share Posted June 14, 2003 Originally posted by MrL_JaKiri A taylor series assumes you can express a function as an infinite sum of the differations of the function, basically. WHat do you mean by differations? Link to comment Share on other sites More sharing options...
JaKiri Posted June 15, 2003 Share Posted June 15, 2003 Originally posted by NSX WHat do you mean by differations? +en. Typographical error. Link to comment Share on other sites More sharing options...
NSX Posted June 18, 2003 Author Share Posted June 18, 2003 So are there any other ways to express "e"? Link to comment Share on other sites More sharing options...
NSX Posted June 18, 2003 Author Share Posted June 18, 2003 Originally posted by dave It's very useful for proving things like Euler's formula (e^(pi * i) +1 = 0) and stuff like that. Not sure I can think of anything else to use it for, but it's mainly used in proofs and such things. And approximations to things like circular/hyperbolic functions etc. What's the value of i? i^2=-1, so that makes i Link to comment Share on other sites More sharing options...
fafalone Posted June 18, 2003 Share Posted June 18, 2003 i is defined as the square root of -1, thats it. Link to comment Share on other sites More sharing options...
JaKiri Posted June 18, 2003 Share Posted June 18, 2003 Originally posted by NSX What's the value of i? i^2=-1, so that makes i i is the square root of minus 1. It's just a number. Link to comment Share on other sites More sharing options...
NSX Posted June 18, 2003 Author Share Posted June 18, 2003 Originally posted by MrL_JaKiri i is the square root of minus 1. It's just a number. Ah..darn; hehe I wanted to just plug it into my calculator and try it. Link to comment Share on other sites More sharing options...
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