Formule de Baza pentru Curbe Plane, Curbe Strambe si Integrala Simpla

CURBE PLANEReprezentari analitice ale curbelor planeO curba plana poate fi reprezentata printr-una din urmatoarele ecuatii:

Ecuatia EXPLICITA : y=f(x) Ec. IMPLICITA : f(x,y)=0 Ec. PARAMETRICE : c(t)=(x(t),y(t)) sau

Ec. VECTORIALA : =x(t)+y(t)

Ec. In COORDONATE POLARE: r=r

ELEMENTUL DE ARC

A. Ec. Parametrica ds=dtB. Ec. Explicita ds=dxC. Ec. In Coordinate Polare ds=d

LUNGIMEA ARCULUI DE CURBA (AB), unde A(x(a),y(a)); B(x(b),y(b))

A. Ec. Parametrica L(AB)=dtB. Ec. Explicita L(AB)= dxC. Ec. In Coordinate Polare L(AB)=d

OBSERVATIE: L(AB)=

ECUATIA TANGENTEI intr-un punct M(,) al curbei plane

1) Ec. Implicita (-)

2) Ec. Parametrica

ECUATIA NORMALEI intr-un punct regulat M()

1) Ec. Implicita

2) Ec. Parametrica

SEGMENTELE TANGENTA, NORMALA ,SUBTANGENTA SI SUBNORMALA1. Ec. Explicita 2. Ec. Parametrica 3. Ec. In Coordinate Polare

MT=|| MT=|| MT=||

MN=|y| MN=|| MN=

ST=|| ST= |y| ST=OT=

SN=|yy| SN=|y| SN=ON=|| CURBURA UNEI CURBE PLANE

1. Ec. Explicita

2. Ec. Parametrica

3. Ec. In Coordinate Polare

RAZA DE CURBURA

R=||PAGE 1

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