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# Calculus

## 3.4 Velocity and other rates of change

### Motion along a line

Relationship between graphs of and the graph of their derivative

## Chapter 2

### 2.1 Rates of Change and Limits

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

### 2.2 Limits involving infinity

Laws

Direct Substitution Property

Finite Limts

More Sandwichs

Infinte Limits

End Behavior models

Seeing Limits

### 2.3 Continuity

Continuity at a point

Continuous Functions

Algebraic Combinations

Composites

Intermediate Value Theorm for continuous functions

### 2.4 Rates of Change and Tanget Lines

Tanget to a Curve

Slope of a Curve

Normal to a Curve

Speed Revisited

## Chapter 3

### 3.2 Differentiablity

Derivatives might not exist

differentiability implies local linearity

Derivatives on Calculator

Differentiability implies Continuity

Intermediate Value Theorem for Derivatives

### 3.3 Rules for Differentiation

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

### 3.5 derivatives of trig functions

Derivative of the Cosine Function

Simple Harmonic Motion

Jerk

Derivatives of other Trig Functions

### 3.6 Chain Rule

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

### 3.7 Implicit Differentiation

Implicitly defined functions

Lenses, Tangents and Normal lines

Derivatives of higher order

Rational Powers of Differentiable functions

### 3.8 Derivaties of Inverse trig functions

Derivatives of inverse functions

Derivatives of the arcsin

Derivative of the arctangent

Derivative of the arcsecant

Derivatives of the other three

### 3.9 Derivaties of Exponential & Logarithmic Functions

Derivative of e^x

Derivative of a^x

Derivative of ln (x)

Derivative of log (x)

Power rule for arbitrary real powers

## General

### Sample Tests

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.

### Recommended Examples

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

## Chapter 1

### 1.1 Lines

Increments

Parallel Lines, Perpendicular lines

Finding Inverse Functions

Equations of Lines

### 1.5 Functions & Logarithms

One-to-one functions

Inverse Functions

Logarithmic Functions

Properties of Logarithms

Applications

### 1.6 Trigonometric Functions

Graphs of Trigonometric Functions

Peroid of trigonometric functions

Even & Odd Trig Functions

Transformations of Trig Functions

Inverse Trig functions