See here for an introduction. It is a guide as to the prerequisite knowledge that you need, but if you feel comfortable with single variable calculus you should be fine. (http://www.x86labs.org:81/forum/index.php/topic,9257.0.html)
The problem here is harder than the problem in the above link.
Suppose (http://www.valhallalegends.com/rule/calcquestions/calc2/func.gif) satisfies (http://www.valhallalegends.com/rule/calcquestions/calc2/cond.gif) for all (http://www.valhallalegends.com/rule/calcquestions/calc2/tin.gif).
Show that
(http://www.valhallalegends.com/rule/calcquestions/calc2/maineq.gif)
Rule's Hint: Again the notation may be confusing, so I will explain. f is continuous in the closed interval from 0,1, and the absolute value of its derivative is less than A in this interval. We want to show the inequality for all natural numbers n (n = 0, 1, 2, ...). It is unlikely you will find a solution to this problem on the internet.
In approximately two weeks I will post my solution to this problem, if there are no attempts.
Quote from: Rule on June 06, 2008, 03:35:05 PM
In approximately two weeks I will post my solution to this problem, if there are no attempts.
Can you post english next to the tex images? Most of the notation you're using is not well-defined.
His notation is standard and the phrase "well-defined" pertains more to definitions (it actually has a strict mathematical meaning but a lot of people use it loosely).
I don't understand though; his hint puts the notation to English.
Quote
Rule's Hint: Again the notation may be confusing, so I will explain. f is continuous in the closed interval from 0,1, and the absolute value of its derivative is less than A in this interval. We want to show the inequality for all natural numbers n (n = 0, 1, 2, ...). It is unlikely you will find a solution to this problem on the internet.
Yeah, but his hint wasn't posted until ten days before I posted that. And I didn't read it.
sorry, but uhhh...
Quote« Last Edit: May 01, 2007, 12:28:30 AM by Rule »
it's been over a year
btw i wouldn't pick on you so much if you weren't friends with myndfyre. pick a side, 'cuz it's war.
Apparently all time-based mathematics that I do come out modulo 1year.
I gave this question to Yoni. He got it in about 20 minutes!!
Quote from: Rule on June 22, 2008, 01:57:56 PM
I gave this question to Yoni. He got it in about 20 minutes!!
Yoni's gifted, though! :P