It is currently Wed Jan 16, 2019 10:25 pm


All times are UTC [ DST ]


Search found 575 matches
Search these results:

Author Message

 Forum: Archives   Topic: A collection of problems in Analysis

Posted: Sun Dec 23, 2018 5:59 pm 

Replies: 4
Views: 1022


Greetings, the current version of the booklet " A collection of problems in Analysis" is out. This is version $11$. Milestone of $500$ exercises is reached , so this new version does not contain any new exercises. However, a new appendix about the Pisot numbers has been added to the bookle...

 Global announcement   Topic: GDPR compliance

 Post subject: GDPR compliance
Posted: Thu May 24, 2018 6:16 pm 

Replies: 0
Views: 584


Dear members and guest of mathimatikoi.org community, as many of you are probably aware the European Union launches on May 25, 2018 a new law under the name $2016/679$ regarding the privacy policy of personal data. We would like to seize this moment to inform you how we handle your personal data: &s...

 Forum: Archives   Topic: A collection of problems in Analysis

Posted: Fri May 18, 2018 12:03 pm 

Replies: 4
Views: 1022


A new version ( version 9 ) is out. Hope you find it entertaining. Awaiting to hear your feedback!

 Forum: Analysis   Topic: Analysis

 Post subject: Re: Analysis
Posted: Wed Feb 07, 2018 7:50 pm 

Replies: 2
Views: 251


Also worth noting Cantor's diagonal argument

 Forum: Analysis   Topic: Analysis

 Post subject: Re: Analysis
Posted: Wed Feb 07, 2018 7:49 pm 

Replies: 2
Views: 251


prove that $(0,1)$ is uncountable Assume that $(0,1)$ is countable. Then you can write $[0,1]=(x_n)_{n \geq 0}$. Do the following steps: - split $[0,1]$ into three equal parts $[0,1/3],[1/3,2/3],[2/3,1]$. Then $x_0$ is not in one of the given intervals. Denote it by $[a_0,b_0]$. - split $[a_0,b_0]$...

 Forum: Real Analysis   Topic: Real analysis

 Post subject: Re: Real analysis
Posted: Wed Feb 07, 2018 7:47 pm 

Replies: 3
Views: 500


Asis ghosh wrote:
what can you say A if LUB A = GLB A ?


I beg your pardon?

 Forum: Real Analysis   Topic: Spivak, Michael : Calculus

Posted: Tue Jan 02, 2018 2:20 pm 

Replies: 1
Views: 271


Yes Michael Spivak's book is a good one although it is densely written ...! I highly recommend it ...!

 Forum: Real Analysis   Topic: On an evaluation of an arctan limit

Posted: Sun Oct 29, 2017 7:37 pm 

Replies: 1
Views: 294


Evaluate the limit

$$\Omega = \lim_{n \rightarrow +\infty} \sum_{k=1}^{n} \frac{\frac{1}{n} \arctan \left ( \frac{k}{n} \right )}{1+2\sqrt{1+\frac{1}{n} \arctan \left ( \frac{k}{n} \right )}}$$

Dan Sitaru

 Forum: Real Analysis   Topic: Limit of a sequence

 Post subject: Limit of a sequence
Posted: Wed Oct 25, 2017 8:02 pm 

Replies: 0
Views: 268


Define the sequence $\{k_n\}_{n \in \mathbb{N}}$ recursively as follows

$$k_0 = \frac{1}{\sqrt{2}} \quad , \quad k_{n+1}={\frac {1-{\sqrt {1-k_{n}^{2}}}}{1+{\sqrt {1-k_{n}^{2}}}}}$$

Evaluate the limit

$$\ell = \lim_{n \rightarrow + \infty} \left(\frac{4}{k_{n+1}}\right)^{2^{-n}}$$

 Forum: General Mathematics   Topic: On an operation

 Post subject: On an operation
Posted: Mon Sep 25, 2017 10:22 pm 

Replies: 0
Views: 352


Define

\begin{equation} x* y = \frac{\sqrt{x^2+3xy+y^2-2x-2y+4}}{xy+4} \end{equation}

Evaluate

$$\mathcal{V} = \left ( \left ( \cdots \left ( \left ( 2007 * 2006 \right )*2005 \right )* \cdots \right ) * 1 \right )$$
Sort by:  
Page 1 of 58 [ Search found 575 matches ]


All times are UTC [ DST ]


Jump to:  
Powered by phpBB® Forum Software © phpBB Group Color scheme created with Colorize It.
Theme created StylerBB.net