Question 2 in Calculus Proof Questions

[Rule]

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.

The problem here is harder than the problem in the above link.

Suppose satisfies for all . 

Show that



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.

[Rule]

In approximately two weeks I will post my solution to this problem, if there are no attempts.

[Camel]

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.

[Ender]

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.

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.

[Camel]

Yeah, but his hint wasn't posted until ten days before I posted that. And I didn't read it.

[Ender]

sorry, but uhhh...

« 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.

[Camel]

Apparently all time-based mathematics that I do come out modulo 1year.

[Rule]

I gave this question to Yoni.  He got it in about 20 minutes!!

[Blaze]

I gave this question to Yoni.  He got it in about 20 minutes!!

Yoni's gifted, though!  :P