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Search found 153 matches
- Tue Dec 18, 2012 2:23 am
- Forum: Introductions
- Topic: আবার দেখা!
- Replies: 9
- Views: 8168
- Sun Nov 18, 2012 3:40 pm
- Forum: Computer Science
- Topic: Calculate ln(x) without math.h
- Replies: 7
- Views: 15860
Re: Calculate ln(x) without math.h
Then write a function exp(x) to calculate (e^x) and use binary search.
- Sat Nov 17, 2012 7:35 pm
- Forum: Computer Science
- Topic: Calculate ln(x) without math.h
- Replies: 7
- Views: 15860
Re: Calculate ln(x) without math.h
Use Maclaurin Series of ln(x).
- Mon Nov 05, 2012 7:55 pm
- Forum: News / Announcements
- Topic: Active users for marathon
- Replies: 23
- Views: 17498
Re: Active users for marathon
Count me in too
And,
if ( forum.getInterestedMembers() >= enough && topic.found() )
{
timeToArrange( onlineCamp, me ) = enough; //
}
And,
if ( forum.getInterestedMembers() >= enough && topic.found() )
{
timeToArrange( onlineCamp, me ) = enough; //
}
- Tue Mar 27, 2012 9:39 pm
- Forum: Algebra
- Topic: Functional Equations PSet : From Very Basic
- Replies: 3
- Views: 3008
Functional Equations PSet : From Very Basic
Here are 50 Functional Equations ( and Inequalities ) from Mathlinks, various contests, own and including basic equations like Cauchy's, Jensen's and D-Alembert's. ( There may be some confusion with the definition of range and co-domain, Wiki says Range $\subseteq$ Co-domain, but somehow not only me...
- Mon Mar 12, 2012 10:10 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO-1983-6
- Replies: 15
- Views: 9866
Re: IMO-1983-6
এই বইয়ে এত বড় ভুল কেমনে করল :O
ওরা লিখসে other cases are similar, কিন্তু $a\le b \le c$ নে, তারপর ওরা যা করসে তা কর, ( মানে ওদের পুরা সমাধানে swap(a,c); ), দেখ সমাধান আসবে না। ওদেরটা ভুল
ওরা লিখসে other cases are similar, কিন্তু $a\le b \le c$ নে, তারপর ওরা যা করসে তা কর, ( মানে ওদের পুরা সমাধানে swap(a,c); ), দেখ সমাধান আসবে না। ওদেরটা ভুল
- Mon Mar 12, 2012 8:03 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO-1983-6
- Replies: 15
- Views: 9866
Re: IMO-1983-6
পোলাপাইন, This is not a symmetric inequality but a cyclic one. So you Can't WLOG assume that $a\ge b\ge c$, instead you can assume WLOG either $a\ge b \ge c$ OR $a\le b\le x$. And, as it is not symmetric, you can't use Muirhead 's inequality.
- Mon Mar 12, 2012 7:33 pm
- Forum: Algebra
- Topic: interesting fun eq
- Replies: 3
- Views: 2945
Re: interesting fun eq
Denote the statement by $P(x,y)$.
$P(x,0),P(0,x)$ imply that $f$ is a Cauchy equation and $f(x^2)=xf(x)$
Now, $(x+1)(f(x)+f(1))=(x+1)f(x+1)=f((x+1)^2)=f(x^2 + 2x + 1)$
$=xf(x)+2f(x)+f(1)$
So, $f(x)=xf(1)$.
$P(x,0),P(0,x)$ imply that $f$ is a Cauchy equation and $f(x^2)=xf(x)$
Now, $(x+1)(f(x)+f(1))=(x+1)f(x+1)=f((x+1)^2)=f(x^2 + 2x + 1)$
$=xf(x)+2f(x)+f(1)$
So, $f(x)=xf(1)$.
- Fri Feb 24, 2012 10:47 pm
- Forum: Geometry
- Topic: (Maybe Very) Hard Geometric Inequality
- Replies: 2
- Views: 2465
(Maybe Very) Hard Geometric Inequality
Let $\triangle ABC$ is a triangle with circumradius $R$. Extend $AB$ to $R$, $BC$ to $P$ an $CA$ to $Q$ and let $D,E,F$ be the midpoints of $BC$, $CA$, $AB$ respectively.
Prove that,
\[\frac{PQ}{AB}+\frac{QR}{BC}+\frac{RP}{CA} \ge \frac{PD+QE+RF}{R}\]
Prove that,
\[\frac{PQ}{AB}+\frac{QR}{BC}+\frac{RP}{CA} \ge \frac{PD+QE+RF}{R}\]
- Fri Feb 24, 2012 10:45 pm
- Forum: College / University Level
- Topic: a problem from IUMO 09
- Replies: 11
- Views: 17561
Re: a problem from IUMO 09
What's your new problem? I couldn't get it.