# Calculus

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Calculus

## 11. 3.4 Velocity and other rates of change

### 11.1. Motion along a line

11.1.1. Relationship between graphs of and the graph of their derivative

## 13. Chapter 2

### 13.1. 2.1 Rates of Change and Limits

13.1.1. Average and Intantaneous Speed

13.1.2. Definition of a limit

13.1.3. Properties of Limits

13.1.3.1. Limit Examples

13.1.4. One sided and two sided limits

13.1.4.1. `1

13.1.5. Sandwich Theorem

### 13.2. 2.2 Limits involving infinity

13.2.1. Laws

13.2.2. Direct Substitution Property

13.2.3. Finite Limts

13.2.4. More Sandwichs

13.2.5. Infinte Limits

13.2.6. End Behavior models

13.2.7. Seeing Limits

### 13.3. 2.3 Continuity

13.3.1. Continuity at a point

13.3.2. Continuous Functions

13.3.3. Algebraic Combinations

13.3.4. Composites

13.3.5. Intermediate Value Theorm for continuous functions

### 13.4. 2.4 Rates of Change and Tanget Lines

13.4.1. Tanget to a Curve

13.4.2. Slope of a Curve

13.4.3. Normal to a Curve

13.4.4. Speed Revisited

## 14. Chapter 3

### 14.1. 3.2 Differentiablity

14.1.1. Derivatives might not exist

14.1.2. differentiability implies local linearity

14.1.3. Derivatives on Calculator

14.1.4. Differentiability implies Continuity

14.1.5. Intermediate Value Theorem for Derivatives

### 14.2. 3.3 Rules for Differentiation

14.2.1. Postive integer powers, multiples, sums, and differences

14.2.2. Products and quotients

14.2.2.1. Derivative of the Sine Function

14.2.3. Negative integer powers of x

14.2.4. Second and higher order derivatives

### 14.3. 3.5 derivatives of trig functions

14.3.1. Derivative of the Cosine Function

14.3.2. Simple Harmonic Motion

14.3.3. Jerk

14.3.4. Derivatives of other Trig Functions

### 14.4. 3.6 Chain Rule

14.4.1. Derivative of a Composite Function

14.4.2. Outside-in rule

14.4.3. Repeated use of the chain rule

14.4.4. Slopes of parametric curves

14.4.5. Power chain rule

14.4.6. New node

14.4.7. New node

### 14.5. 3.7 Implicit Differentiation

14.5.1. Implicitly defined functions

14.5.2. Lenses, Tangents and Normal lines

14.5.3. Derivatives of higher order

14.5.4. Rational Powers of Differentiable functions

### 14.6. 3.8 Derivaties of Inverse trig functions

14.6.1. Derivatives of inverse functions

14.6.2. Derivatives of the arcsin

14.6.3. Derivative of the arctangent

14.6.4. Derivative of the arcsecant

14.6.5. Derivatives of the other three

### 14.7. 3.9 Derivaties of Exponential & Logarithmic Functions

14.7.1. Derivative of e^x

14.7.2. Derivative of a^x

14.7.3. Derivative of ln (x)

14.7.4. Derivative of log (x)

14.7.5. Power rule for arbitrary real powers

## 17. General

### 17.2. Recommended Examples

17.2.1. Solutions

## 18. Chapter 1

### 18.1. 1.1 Lines

18.1.1. Increments

18.1.2. Parallel Lines

18.1.2.1. Perpendicular lines

18.1.3. Finding Inverse Functions

18.1.4. Equations of Lines

### 18.2. 1.5 Functions & Logarithms

18.2.1. One-to-one functions

18.2.2. Inverse Functions

18.2.3. Logarithmic Functions

18.2.4. Properties of Logarithms

18.2.5. Applications

### 18.4. 1.6 Trigonometric Functions

18.4.1. Graphs of Trigonometric Functions

18.4.2. Peroid of trigonometric functions

18.4.3. Even & Odd Trig Functions

18.4.4. Transformations of Trig Functions

18.4.5. Inverse Trig functions