Chapters 12-13 Flashcards
Paraboloids
Elliptic z=(x/a)^2+(y/a)^2
Hyperbolic z=(x/a)^2 -(x/b)^2
Elliptic cone
(x/a)^2+(y/b)^2=(z/c)^2
Hyperboloids
One sheet: (x/a)^2 +(y/b)^2 =(z/c)^2 +1
Two sheets: (x/a)^2 + (y/b)^2 =(z/c)^2 -1
Ellipsoid
(x/a)^2+(y/b)^2 +(z/c)^2 =1
Elliptic cylinder
(x/a)^2+ (y/b)^2=1
Hyperbolic cylinder
(x/a)^2 - (y/b)^2 =1
Parabolic cylinder
y=ax^2
Unit vector
[V/||V||]
Used to indicate direction
Use e_v to scale a nonzero vector v= to obtain a unit vector pointing in the same direction.
*******[1/||V||]xV
Cos(0)=?
1
Sin(0)=?
0
Cos(pi/6)=?
Radical(3)/2
Sin(pi/6)=?
1/2
Cos(pi/4)=?
1/radical(2)
Sin(pi/4)=?
1/radical(2)
Cos(pi/3)=?
1/2
Sin(pi/3)=?
Radical(3)/2
Cos(pi/2)=?
0
Sin(pi/2)=?
1
Cos(2pi/3)=?
-1/2
Sin(2pi/3)=?
Radical(3)/2
Cos(3pi/4)=?
-1/radical(2)
Sin(3pi/4)=?
1/radical(2)
Cos(5pi/6)=?
-radical(3)/2
Tangent line
R(t0)-> L(t)=r(t0)+t(r’(t0)
Arc length
Integral from a to b of ||r’(t)||
