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Question 2 in Calculus Proof Questions

Started by Rule, May 01, 2007, 12:18:25 AM

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Rule

May 01, 2007, 12:18:25 AM Last Edit: May 01, 2007, 12:28:30 AM by 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

#1
June 06, 2008, 03:35:05 PM
In approximately two weeks I will post my solution to this problem, if there are no attempts.

Camel

#2
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.

<Camel> i said what what
<Blaze> in the butt
<Camel> you want to do it in my butt?
<Blaze> in my butt
<Camel> let's do it in the butt
<Blaze> Okay!

Ender

#3
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.

Camel

#4
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.

<Camel> i said what what
<Blaze> in the butt
<Camel> you want to do it in my butt?
<Blaze> in my butt
<Camel> let's do it in the butt
<Blaze> Okay!

Ender

#5
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.

Camel

#6
June 12, 2008, 11:29:52 PM
Apparently all time-based mathematics that I do come out modulo 1year.

<Camel> i said what what
<Blaze> in the butt
<Camel> you want to do it in my butt?
<Blaze> in my butt
<Camel> let's do it in the butt
<Blaze> Okay!

Rule

#7
June 22, 2008, 01:57:56 PM
I gave this question to Yoni.  He got it in about 20 minutes!!

Blaze

#8
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
And like a fool I believed myself, and thought I was somebody else...
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