Multivariable - All things to memorize

lim sin(x)/x = ?

lim sin(x)/x = 1

Continuous?

Lim (x,y) of f(x,y) = f(a,a)

(1 - cos u) / u = ?

(1 - cos u) / u = 0

Curvature

|a(t) x v(t)| / |v(t)|³

Directional Derivative

∇f · Û

Max increase where?

|+∇f|

Max decrease where?

|-∇f|

Dot Product

a ⋅ b = |a||b| cos θ

Implicit

dz / dx = -Fx / Fz

Level Curves

z = k

2D Shapes

x², y² - Same Sign = Ellipses/Circles; x, y (0 squared variable) = Lines; 2 squared variables - Differnt Sign = Hyperbolas; 1 squared variable = Parabolas