## 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

Problems 1-8
These problems are basically definitions that you need to know for this section. It would be a good idea not only to look them up to answer these questions, but also to study.

Problems 9-13
See the box … 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

Problems 1-2
There are many problems throughout the text labeled IN YOUR OWN WORDS. Just relax; do not be afraid to give your opinion. For the most part, these questions do not have “right” or “wrong” answers. You should spend … 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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