Problems from dhk div 2010!!
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
$1$)
If $x$ is very very very small $sin x\approx x$. An operator $S_n$ is defined such that
$S_n(x)= sin\cdot sin\cdot sin\cdot ....sin x $(a total of $n, sin$ operators are included here). For
sufficiently large $n, S_n(x) \approx S_{n-1}(x)$. In that case, express cos $(S_n(x))$ as the
nearest rational value.
Please help me understand and solve the prob.
If $x$ is very very very small $sin x\approx x$. An operator $S_n$ is defined such that
$S_n(x)= sin\cdot sin\cdot sin\cdot ....sin x $(a total of $n, sin$ operators are included here). For
sufficiently large $n, S_n(x) \approx S_{n-1}(x)$. In that case, express cos $(S_n(x))$ as the
nearest rational value.
Please help me understand and solve the prob.
Last edited by Labib on Thu Dec 30, 2010 10:34 pm, edited 2 times in total.
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Re: Problems from dhk div 2010!!
yap , i didnt even understand this problem .... i wasted 14 mins
- Tahmid Hasan
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Re: Problems from dhk div 2010!!
for the small x,the value of $$x=0 $$ and $$S_n(x)=0$$
that's all i can say
that's all i can say
বড় ভালবাসি তোমায়,মা
Re: Problems from dhk div 2010!!
Tahmid, you have reached the right answer, but in a wrong way...
The question doesn't require x to be small or 0. The result is 1 and it needs quite jumpy travels to reach the answer rigorously. However, the question was meant to judge your intution
The question doesn't require x to be small or 0. The result is 1 and it needs quite jumpy travels to reach the answer rigorously. However, the question was meant to judge your intution
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor
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Re: Problems from dhk div 2010!!
I didnt understood that nSn(x) Sn-1(x). My ans is like that sin sin sin sin(x)=x(because x is so small so sin x =x) so Sn(x)=x and cos Sn (x)=cos x=1
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Re: Problems from dhk div 2010!!
Amar ta ki vul holo.confused
Re: Problems from dhk div 2010!!
The problem never said that $x$ has to be small. So you have to think in a generalized manner. You have reached the correct answer. But your understanding is faulty.
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor
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Re: Problems from dhk div 2010!!
আরে বাবা, আর কিছু না পারলে x এর একটা মান ধইরা দশ-বারোটা চেষ্টা কইরা দেখো!
If computers have no doors or fences, who needs Windows and Gates?
Re: Problems from dhk div 2010!!
আমার সমাধান এরকম,
কোথাও কোনো ভুল করলাম কি ?
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
Re: Problems from dhk div 2010!!
A article was published about this article on 'Gonit School' of The prothom-alo.....