f, g ,h si g(x)=f(x)sin x si h(x)=f(x)cos x
Moderators: Bogdan Posa, Beniamin Bogosel, Marius Dragoi
-
Cezar Lupu
- Site Admin
- Posts: 612
- Joined: Wed Sep 26, 2007 2:04 pm
- Location: Bucuresti sau Constanta
- Contact:
f, g ,h si g(x)=f(x)sin x si h(x)=f(x)cos x
Fie \( f, g,h :\mathbb{R}\to\mathbb{R} \) astfel incat sa avem relatiile: \( g(x)=f(x)\sin x \) si \( h(x)=f(x)\cos x \) pentru orice \( x\in\mathbb{R} \). Sa se arate ca daca \( g, h \) admit primitive, atunci \( f \) admite primitive.
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
-
Marius Mainea
- Gauss
- Posts: 1077
- Joined: Mon May 26, 2008 2:12 pm
- Location: Gaesti (Dambovita)
Se foloseste urmatoare lema:
Daca \( f,g:I\rightarrow\mathbb{R},\ I\subset\mathbb{R} \) interval, g derivabila cu derivata continua si f admite primitive, atunci \( h=f\cdot g \) admite primitive.
Apoi se poate demonstra si afirmatia:
(**) "Daca functiile \( u(x)=f(x)\cdot\cos^3(x),\ x\in\mathbb{R} \) si \( v(x)=f(x)\cdot\sin^3(x),\ x\in\mathbb{R} \) admit primitive, atunci functia f admite primitive."
Daca \( f,g:I\rightarrow\mathbb{R},\ I\subset\mathbb{R} \) interval, g derivabila cu derivata continua si f admite primitive, atunci \( h=f\cdot g \) admite primitive.
Apoi se poate demonstra si afirmatia:
(**) "Daca functiile \( u(x)=f(x)\cdot\cos^3(x),\ x\in\mathbb{R} \) si \( v(x)=f(x)\cdot\sin^3(x),\ x\in\mathbb{R} \) admit primitive, atunci functia f admite primitive."