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Calculus
by Joan Keating
# Calculus

## 1.4 Parametric Equations

### Relations

### Circles

### Ellipses

### Lines & Other Curves

## Functions

## Average Rates of Change

## Applications

## 1.2 Functions & Graphs

### Domain & Range

### Viewing & Intrepreting Graphs

### Even & Odd Functions

### Piecewise Functions

### Absolute Value Function

### Composite Functions

## Radian Measure

## Slope of a line

## 1.3 Exponential Functions

### Exponential Growth & Decay

### The Number e

### Applications

## Instantaneous rates of change

## 3.1 Derivative of a Function

### Definition of a derivative

### Graphing Derivative from Data

### One-sided derivatives

## 3.4 Velocity and other
rates of change

### Motion along a line

### Sensitivity to change

### Derivatives in Economics

## Derivative Notation

## Chapter
2

### 2.1 Rates of Change and Limits

### 2.2 Limits involving infinity

### 2.3 Continuity

### 2.4 Rates of Change
and Tanget Lines

### Review

## Chapter 3

### 3.2 Differentiablity

### 3.3 Rules for Differentiation

### 3.5 derivatives of trig functions

### 3.6 Chain Rule

### 3.7 Implicit Differentiation

### 3.8 Derivaties of
Inverse trig functions

### 3.9 Derivaties of
Exponential & Logarithmic
Functions

### Key terms & Review

## Chapter 4

## Chapter 5

## General

### Sample Tests

### Recommended Examples

## Chapter 1

### 1.1 Lines

### 1.5 Functions & Logarithms

### Key Terms & Review

### 1.6 Trigonometric Functions

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Relationship between graphs of and the graph of their derivative

A Secant line is a line segment that connects to two points on a function. Its slope provides the average rate of change of the function. A Tangent line on the other hand is a line that touches only one point on the graph, and provides the instantaneous rate of change.

Average and Intantaneous Speed

Definition of a limit

Properties of Limits, Limit Examples

One sided and two sided limits, `1

Sandwich Theorem

Laws

Direct Substitution Property

Finite Limts

More Sandwichs

Infinte Limits

End Behavior models

Seeing Limits

Continuity at a point

Continuous Functions

Algebraic Combinations

Composites

Intermediate Value Theorm for continuous functions

Tanget to a Curve

Slope of a Curve

Normal to a Curve

Speed Revisited

Derivatives might not exist

differentiability implies local linearity

Derivatives on Calculator

Differentiability implies Continuity

Intermediate Value Theorem for Derivatives

Postive integer powers, multiples, sums, and differences

Products and quotients, Derivative of the Sine Function

Negative integer powers of x

Second and higher order derivatives

Derivative of the Cosine Function

Simple Harmonic Motion

Jerk

Derivatives of other Trig Functions

Derivative of a Composite Function

Outside-in rule

Repeated use of the chain rule

Slopes of parametric curves

Power chain rule

New node

New node

Implicitly defined functions

Lenses, Tangents and Normal lines

Derivatives of higher order

Rational Powers of Differentiable functions

Derivatives of inverse functions

Derivatives of the arcsin

Derivative of the arctangent

Derivative of the arcsecant

Derivatives of the other three

Derivative of e^x

Derivative of a^x

Derivative of ln (x)

Derivative of log (x)

Power rule for arbitrary real powers

I chose this link because it provides sample tests provided by my teacher, these tests have helped me so far in the semester, so I think they will help in my preparation for the final. I consider this scholarly or at least semi scholarly, my professor is the head of the Math Department at CCU, James Solazzo.

This PDF is a list of exercises my teacher has recommended, these will help me become familiar with the types of problems, and skill sets I will need to be prepared for the final. I consider this scholarly or at least semi scholarly, my professor is the head of the Math Department at CCU, James Solazzo.

Solutions

Increments

Parallel Lines, Perpendicular lines

Finding Inverse Functions

Equations of Lines

One-to-one functions

Inverse Functions

Logarithmic Functions

Properties of Logarithms

Applications

Graphs of Trigonometric Functions

Peroid of trigonometric functions

Even & Odd Trig Functions

Transformations of Trig Functions

Inverse Trig functions