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Analiza Matematica

 
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IoanaTw



Joined: 22 Sep 2013
Posts: 3

PostPosted: Sun Sep 22, 2013 2:09 pm    Post subject: Analiza Matematica Reply with quote

Aratati ca urmatoarele multimi sunt marginite:

A={ (2n^2+n)/(2n^2+1) | x apartine N }

B={ (3n/ (n+1) | x apartine N } .
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Adriana Nistor
Thales


Joined: 07 Aug 2008
Posts: 116
Location: Bucuresti

PostPosted: Sun May 11, 2014 1:13 pm    Post subject: Reply with quote

Pt multimea A=\{ \frac{2n^2+n}{2n^2+1}| n\in N\} avem ca orice element \frac{2m^2+m}{2m^2+1} se afla intre 0 si 2, pentru ca:
\frac{2m^2+m}{2m^2+1}\leq 2<=> 2m^2+m\leq 4m^2+2<=> m\leq 2m^2+2 , ceea ce e mereu adevarat \forall m\in N
(ca demonstratie: 2m^2+2=2(m^2+1)\geq 2*2m=4m>m. La prima inegalitate am folosit inegalitatea mediilor)
Pt multimea B=\{\frac{3n}{n+1}|n\in N} avem ca orice element \frac{3m}{m+1} se afla intre 0 si 3, pentru ca:
\frac{3m}{m+1}\leq 3 <=> 3m\leq 3(m+1), adica 3m\leq 3m+3, evident adevarat.
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