## 18.1 Outline

1. What is Calculus?
1. Calculus is the mathematics of motion and change.
2. The three main ideas of calculus are limit, derivative, and integral
1. Achilles and the tortoise
2. limit of a sequence
3. The derivative: the tangent
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## Homework Hints 15-4

### Note: Homework Hints are given only for the Level 1 and Level 2 problems.

However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 … See the whole entry

## 15.4 Outline

1. Introduction
1. definition
2. model
2. Geometric definition of conic sections
1. parabola
1. focus
2. directrix
3. axis
4. vertex
2. ellipse
1. foci
2. major axis
3. center
4. minor axis
3. circle
1. center
4. hyperbola
1. transverse axis
2. center
3. conjugate axis
3. Algebraic definition of conic sections
1. general form
1. first-degree equation
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## Individual Research Project Section 8.1

### Project 8.1

Suppose you drive you car in a roundabout traffic circle that is 100 ft in diameter. Assume your tires are on the circumference of the circle, and also assume that your car is six feet wide.

• If you
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## Homework Hints 8-2

### Note: Homework Hints are given only for the Level 1 and Level 2 problems.

However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 … See the whole entry

## 8.2 Outline

1. Rectangles
1. define area
2. define square unit
3. formulas
1. rectangle
2. square
2. Parallelograms
1. definition
2. formula
3. derivation of formula
3. Triangles
1. formula
2. derivation of formula
4. Trapezoids
1. definition
2. formula
3. derivation of formula
5. Circles
1. formula
2. derivation of formula
6. Applications
1. conversion application
2. acre definition
3. conversion of
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## 7.6 Outline

1. Golden rectangles
1. definition
2. divine proportion
3. tau
2. Mathematics and art
1. golden ratios in art
2. proportions of the human body
3. spiral constructed using a golden rectangle
3. Projective geometry
1. Duccio’s Last Supper
2. Hogarth’s Perspective Absurdities
3. false perspective
4. Masaccio’s The Holy Trinity
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