Clan x86

General Forums => Academic / School => Math and Other Problems => Topic started by: Rule on May 01, 2007, 12:18:25 am

Title: Question 2 in Calculus Proof Questions
Post by: Rule on May 01, 2007, 12:18:25 am
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.
Title: Re: Question 2 in Calculus Proof Questions
Post by: 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.
Title: Re: Question 2 in Calculus Proof Questions
Post by: Camel on June 10, 2008, 02:41:43 am
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.
Title: Re: Question 2 in Calculus Proof Questions
Post by: Ender on June 10, 2008, 03:22:20 am
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.
Title: Re: Question 2 in Calculus Proof Questions
Post by: Camel on June 11, 2008, 02:18:57 am
Yeah, but his hint wasn't posted until ten days before I posted that. And I didn't read it.
Title: Re: Question 2 in Calculus Proof Questions
Post by: Ender on June 11, 2008, 04:51:56 am
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.
Title: Re: Question 2 in Calculus Proof Questions
Post by: Camel on June 12, 2008, 11:29:52 pm
Apparently all time-based mathematics that I do come out modulo 1year.
Title: Re: Question 2 in Calculus Proof Questions
Post by: Rule on June 22, 2008, 01:57:56 pm
I gave this question to Yoni.  He got it in about 20 minutes!!
Title: Re: Question 2 in Calculus Proof Questions
Post by: Blaze on June 22, 2008, 09:28:27 pm
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