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Calculus (General) FormulasCalculus (General) Formulas "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #2 20060330 10:24:17
Re: Calculus (General) FormulasLast edited by Ricky (20060405 02:25:21) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20060402 17:13:48
Re: Calculus (General) FormulasIf x=f(t), then dy/dx = (dy/dt)/(dx/dt) d(logx)/dx = 1/x d(Sinx)/dx = Cosx d(Cosx)/dx = Sinx d(tanx)/dx = Sec²x d(cotx)/dx = Cosec²x d(secx)/dx = secxtanx d(cosecx)/dx = CosecxCotx Character is who you are when no one is looking. #4 20060405 02:23:46
Re: Calculus (General) Formulas"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #5 20060407 00:19:24
Re: Calculus (General) FormulasIn the last Ricky post there is a little mistake: IPBLE: Increasing Performance By Lowering Expectations. #6 20060409 16:25:42
Re: Calculus (General) FormulasFundamental limits , a>0 ,a>0 , a>0 , a>0, n∈N Character is who you are when no one is looking. #7 20060410 02:52:13
Re: Calculus (General) FormulasHold it, the limit of tan 1/x as x approaches zero is pi/2? That doesn't seem right. A logarithm is just a misspelled algorithm. #8 20060410 22:42:20
Re: Calculus (General) Formulasand another fomula say it's x/2 ??? X'(yXβ)=0 #9 20060411 00:07:58
Re: Calculus (General) Formulaslimit as x approaches 0 of tan(1/x) is undefined. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #10 20060411 00:41:49
Re: Calculus (General) Formulas[Thank you, Mikau, George and Ricky. I have incorporated the correction.] where p and q are integers. Character is who you are when no one is looking. #11 20060411 01:07:55
Re: Calculus (General) FormulasSome Important Expansions: for 1<x<1 for every positive value of x<1. Character is who you are when no one is looking. #12 20060411 03:54:26
Re: Calculus (General) Formulas
I don't think thats correct. Yes the limit of tan (1/x) as x approaches zero is undefined, but the limit of arctan (1/x) as x approaches zero IS pi/2. Think about it, if θ is an angle in a right triangle, and the side opposite θ is 1 and the side adjacent to θ is x, as x approaches zero, θ aproaches 90 from the left. A logarithm is just a misspelled algorithm. #13 20060411 05:22:58
Re: Calculus (General) FormulasThis isn't rigourous, but more of a way to think about it. limit 1/x as x goes to 0 from the positive side is positive infinity. So what we really want to find is the limit of arctan(x) as x goes to infinity, which is pi/2. Last edited by Ricky (20060411 05:25:59) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #14 20060411 08:35:56
Re: Calculus (General) FormulasOh, right. Sorry, I forgot no one specified which side it approaches zero from so the left hand limit has to equal the right hand limit, for a limit to exist. A logarithm is just a misspelled algorithm. #15 20060807 17:20:29
Re: Calculus (General) FormulasMaclaurin/Taylor Series Trigonometric Functions See bottom of post for definition of B_{n}. See bottom of post for definition of B_{n}. See bottom of post for definition of E_{n}. See bottom of post for definition of B_{n}. Hyperbolic Functions See bottom of post for definition of B_{n}. See bottom of post for definition of B_{n}. See bottom of post for definition of E_{n}. See bottom of post for definition of B_{n}. B_{n}: The Bernoulli Numbers The Bernoulli numbers B_{n} are a sequence of special rational numbers. Their derivation is outside the scope of this thread, but an explanation may be offered elsewhere upon sufficient demand. The first few Bernoulli numbers are(note that for odd n other than 1, B_{n} = 0): E_{n}: The Euler Numbers The Euler numbers E_{n} are a sequence of special numbers. Their derivation is outside the scope of this thread, but an explanation may be offered elsewhere upon sufficient demand. The first few Euler numbers are(note that for all odd n, E_{n} = 0): Last edited by Zhylliolom (20060807 20:51:43) #16 20081223 12:14:20
Re: Calculus (General) FormulasFinding Derivatives By First Principles "If your going through hell, keep going." 