MTH 209 Exam 3 Formulas (MathGPT)

Unit Tangent Vector

Arc Length of a Curve on [a,b]

Arc Length Function (from base point t0)

Reparameterization Property

Curvature (parameterized by arc length s)

Curvature (using Unit Tangent Vector)

Curvature (straight line)

Curvature (Circle of Radius R)

Curvature (Helix = <acost,asint,bt>)

Two-Path Test for Non-Existence

First Partial Derivatives

Second Partial Derivatives

Mixed Second Partials (Clairaut’s Theorem)

Gradient Vector

Directional Derivative (General Formula with unit vector)

Normalizing a given vector

Vector between points P and Q

Given an angle with positive x-axis

Maximum Rate of Increase

Maximum Rate of Decrease

Zero Rate of Change

Tangent Plane of Explicit Surface

Tangent Plane of Implicit Surface

Magnitude of Vector

Dot Product