mateforum.ro Forum Index mateforum.ro

 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

inegalitate

 
Post new topic   Reply to topic    mateforum.ro Forum Index -> Clasa a XI-a -> Algebra
View previous topic :: View next topic  
Author Message
Adriana Nistor
Thales


Joined: 07 Aug 2008
Posts: 116
Location: Bucuresti

PostPosted: Thu Feb 10, 2011 11:43 pm    Post subject: inegalitate Reply with quote

Sa se demonstreze ca (\frac{x}{\sin x})^{tg x-x}>(\frac{tg x}{x})^{x-\sin x} oricare ar fi x\in(0,\frac{\pi}{2})
Back to top
View user's profile Send private message Yahoo Messenger
bossmath



Joined: 19 Feb 2011
Posts: 1

PostPosted: Sat Feb 19, 2011 1:38 pm    Post subject: Raspuns? Reply with quote

Asa si raspunsul la aceasta problema care este? Rezolvarea?
Back to top
View user's profile Send private message
Costica Ambrinoc
Euclid


Joined: 01 Feb 2010
Posts: 20
Location: Rm Sarat

PostPosted: Sat Feb 19, 2011 3:37 pm    Post subject: Reply with quote

Prin logaritmare si tinand seama ca tgx>x si   sinx<x se obtine  \frac{lnx-lnsinx}{x-sinx}>\frac{lntgx-lnx}{tgx-x}
Se aplica Lagrange ptr lnx pe intervalul  [sinx,x] si apoi pe intervalul [x,tgx] si se obtine ca exista  sinx<c_1<x<c_2<tgx
astfel incat \frac{1}{c_1}=\frac{lnx-lnsinx}{x-sinx} si \frac{1}{c_2}=\frac{lntgx-lnx}{tgx-x}
Inegalitatea din enunt devine \frac{1}{c_1}>\frac{1}{c_2} care e adevarata.
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    mateforum.ro Forum Index -> Clasa a XI-a -> Algebra All times are GMT + 2 Hours
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum



Powered by phpBB © 2001, 2005 phpBB Group