Matem´atica 2 - C´at. Zorzoli F´ormulas
sen(α) = O
H,cos(α) = A
H,tan(α) = O
Aa2=b2+c2a2=b2+c2−2·b·c·cos( ˆ
A)a
sen( ˆ
A)=b
sen( ˆ
B)=c
sen( ˆ
C)p=a+b+c
2A=pp·(p−a)·(p−b)·(p−c)
v ·w =vx·wx+vy·wy+vz·wz=||v|| · || w|| · cos α v ×w = (vy·wz−vz·wy;vz·wx−vx·wz;vx·wy−vy·wx)
(x;y;z)=(x0;y0;z0) + k(vx;vy;vz)
x=x0+k·vx
y=y0+k·vy
z=z0+k·vz
x−x0
vx
=y−y0
vy
=z−z0
vz
ax +by +cz +d= 0
(x−h)2
a2+(y−k)2
b2= 1 ´o (x−h)2
b2+(y−k)2
a2= 1 c2=a2−b2e=c
aF1,2= (h±c;k) ´o F1,2= (h;k±c)
(x−h)2
a2−(y−k)2
b2= 1 ´o (y−k)2
a2−(x−h)2
b2= 1 c2=a2+b2e=c
aF1,2= (h±c;k) ´o F1,2= (h;k±c)y−k=±b
a(x−h) ´o y−k=±a
b(x−h)
(x−h)2= 2p(y−k) ´o (y−k)2= 2p(x−h)F= (h, k +p
2), d :y=k−p
2´o F= (h+p
2, k), d :x=h−p
2(x−h)2+ (y−k)2=r2
y−f(x0) = f′(x0)·(x−x0)y−f(x0) = −1
f′(x0)·(x−x0)x(t), v(t) = x′(t), a(t) = x′′(t)
·A=Zb
a
(f(x)−g(x)) dx Vx=πZb
a
(f(x))2dx Vy=πZd
c
(g(y))2dy C =Zb
ap1+(f′(x))2dx mT=δA =δZb
a
(f(x)−g(x)) dx
M(1)
x=δ
2Zb
a
(f2(x)−g2(x)) dx M(1)
y=δZb
a
x(f(x)−g(x)) dx M(2)
x=δ
3Zb
a
(f3(x)−g3(x)) dx M(2)
y=δZb
a
x2(f(x)−g(x)) dx G = (xG;yG) = M(1)
y
mT
;M(1)
x
mT!
P(A) = N°de casos favorables
N°de casos totales P(A∪B) = P(A) + P(B)−P(A∩B)P(A|B) = P(A∩B)
P(B)C+V=A+ 2 ϕ=1 + √5
2