MVC midterm 1

f’[x] when given f[x] is some function described by {x[t], y[t]}

y’[t]/x’[t]

Dot product

x1y1 + x2y2 + x3y3

||x|| ||y|| Cos[theta]

Length of cross product

||A|| ||B|| Sin[theta]

XpushalongY

(X.Y)/(Y.Y)Y

Speed

Radical(P’[t] . P’[t])

Equation of a plane

{(x, y, z) - point} . normal = 0

A(x-x0) + B(y-y0) + C(z-z0) = 0

Gauss green

Integral(a to b) (m[x[t], y[t]] x’[t] + n[x[t], y[t]] y’[t])

{y’[t], -x’[t]}

• right footed normal

• always points out if counterclockwise 

Mainunitnormal[t]

Binormal[t]

Unittan[t]

Tangent lines in 2D

Tangent planes in 3D

Total derivative (2D Chain rule)

Determining critical points

Hessian determinant

Direction derivative

Lagrange multipliers

Gauss green conditions to transform a double integral to a single integral

Formula for gradf[x, y]

Relationship between a level curve and gradient vectors

Equation of a line

Average value and centroid