Outline

# Calculus 1 Graphical Illustrations

The curve is called the "folium of Descartes" ("folium" is Latin for "leaf"). This equation first came out in a letter from Descartes to Fermat (Fermat was a lawyer by profession, but did mathematics as a hobby). Fermat claimed to have a method to find tangent lines to any curve, and Descartes invented this curve as a challenge to Fermat. Fermat was successful in finding tangent lines to the curve. Today, however, the problem of finding tangent lines is straightforward, due to the invention of calculus sometime later. This event was notable enough in the history of calculus that it is memorialized in the Albanian postage stamp above.
Source: http://goo.gl/JhLTgE

## Table of Contents

### Limits and Derivatives

- Section 2.1 - The Tangent Line
- Section 2.1: Approximating the Slope of a Tangent Line
- Section 2.2 - Intuitive Definition of Limits of a Function
- Section 2.2: Intuitive Definition of Limits of a Function
- Section 2.2: Limit Does Not Exist
- Section 2.2 Infinite Limits
- Section 2.3: One-sided Limits
- Section 2.6: Vertical Asymptotes
- Section 2.5: Intermediate Value Theorem
- Section 2.6: Horizontal Asymptote
- Section 2.6 Horizontal and Vertical Asymptote
- Section 2.7: Differentiability
- Section 2.8: Derivative as a Function
- Section 2.8: Higher Derivatives

### Differentiation Rules

- Section 3.2: Tangent Line to a Curve (Quotient Rule)
- Section 3.3 - Trig Limits - Squeeze Theorem
- Section 3.3: Derivative of Sine Function
- Section 3.3: Derivative Application
- Section 3.4: Motion of a Spring
- Section 3.5: Implicit Differentiation - Descartes' Leaf
- Section 3.5: Implicit Differentiation (Cramer, 1750)
- Section 3.5: Inverse Tangent Function
- Section 3.10: Linear Approximation
- Section 3.11 Hyperbolic Functions
- St Louis Gateway Arch

### Derivative Applications

### Integrals