7.2 The tangent divides rates of change · Parametric Equations · Visual Calculus

7.2Parametric slope

∫Visual Calculus

Chapter 2 · Applications of Integration

2.1-2.2Areas & Slicing

2.3-2.4Shells & Arc Length

2.5Physical Applications

2.6Centers of Mass

2.7-2.9Log, Exp & Hyperbolic

Chapter 3 · Techniques of Integration

3.1-3.4Techniques I

3.5-3.7Techniques II

Chapter 5 · Sequences and Series

5.1-5.3Sequences & Series I

5.4-5.6Sequences & Series II

Chapter 7 · Parametric Equations and Polar Coordinates

7.1-7.2Parametric Curves

7.1Moving trace 7.1Eliminate t 7.1Cycloid roulette 7.2Parametric slope 7.2Second derivative 7.2Swept area 7.2Arc length 7.2Surface area

7.3-7.4Polar Curves

Chapter 6 · Power Series

6.1-6.2Power Series I

6.3-6.4Power Series II

Home Calculus IISections 7.1-7.27.2 The tangent divides rates of change

7.2

The tangent divides rates of change

2

Interactive view

Previous · 7.1Rolling circles draw roulette curves Next · 7.2Concavity needs another division by x prime

Live setup

SymPy check = 0.5

SymPy checks

Cycloid arch width6.2831853072

Ellipse semi-major axis4

Astroid cusp count4

Parametric slope at t = 20.5

Parametric second derivative at t = 2-0.0625

Cycloid arch area9.4247779608

Radius-3 semicircle length9.4247779608

Unit sphere surface area12.5663706144