Calculus 3 - Exam 3 Study Guide

How to find limit of vector function

Limit of each equation. Apply L’hops rule if necessary. Answer should be in vector equation form

Velocity vector

r’(t)

Acceleration vector

r’’(t)

Speed

|v(t)|d

Direction

v(t)/|v(t)|

How to find the parametric equation of the line tangent to curve?

Find position r(t). Find direction vector r’(t). Form equation where scalars are r(t) and vectors are r’(t)

∫ u dv =

uv-∫v du

Tabular method for integration by parts

1. Set up two columns: u and dv.

2. Derive the first column, integrate the second column till u becomes 0.

3. Connect the term diagonally with alternating signs.

Arc length with three components

Unit tangent vector

velocity/magnitude of velocity

Curvature (k)

Magnitude of Cross product of velocity and acceleration/magnitude of velocity cubed