# Calculus l

Presents a study of analytic geometry, limits, continuity, the calculus of algebraic, trigonometric, exponential and logarithmic functions, as well as applications of the derivative and integral. Each topic is taught geometrically, numerically, and algebraically. The course explores mathematical concepts, methods and applications from life issues, science, business, finance and environmental issues.
Prerequisite: College Algebra and Trigonometry or Precalculus with Trigonometry with a grade of C or better.

## Chapter 1

Functions

Lessons Homework HW Quiz
1.1 Representations of a Function 1.1 1.1
1.2 Polynomials, Radical and Rational Functions 1.2 1.2
1.3 Exponential and Logarithmic Functions 1.3 1.3
1.4 Trigonometric Functions 1.4 1.4
1.5 Piecewise Functions 1.5 1.5
1.6 Operations on Functions 1.6 1.6
1.7 Inverse Functions 1.7 1.7
1.8 Properties of Functions 1.8 1.8
1.9 Evaluating and Graphing Functions Using the Calculator 1.9 1.9
Chapter 1 Test

## Chapter 2

Limits and Continuity

Lessons Homework HW Quiz
2.1 Rates of Change and Tangents 2.1 2.1
2.2 The Limit of a Function 2.2 2.2
2.3 Limit Laws 2.3 2.3
2.4 Continuity 2.4 2.4
2.5 Limits at Infinity 2.5 2.5
2.6 Using the Calculator to Evaluate Limits 2.6 2.6
Chapter 2 Test

## Chapter 3

Differentiation

Lessons Homework HW Quiz
3.1 Tangents and the Derivative at a Point 3.1 3.1
3.2 The Derivative as a Function 3.2 3.2
3.3 Differentiation Formulas 3.3 3.3
3.4 Derivatives of Trigonometric Functions 3.4 3.4
3.5 The Chain Rule 3.5 3.5
3.6 Implicit Differentiation 3.6 3.6
3.7 Rates Of Change 3.7 3.7
3.8 Using the Calculator to Evaluate the Derivative 3.8 3.8
Chapter 3 Test

## Chapter 4

Applications of Derivatives

Lessons Homework HW Quiz
4.1 Related Rates 4.1 4.1
4.2 Maximum and Minimum Values of a Function 4.2 4.2
4.3 The Mean Value Theorem 4.3 4.3
4.4 Graphs of Functions 4.4 4.4
4.5 Optimization 4.5 4.5
4.6 Linear Approximations and Differentials 4.6 4.6
4.7 Newton's Method 4.7 4.7
4.8 Using the Calculator to Find Extrema 4.8 4.8
Chapter 4 Test

## Chapter 5

Integration

Lessons Homework HW Quiz
5.1 Antiderivatives and the Indefinite Integral 5.1 5.1
5.2 Area Under a Curve 5.2 5.2
5.3 The Definite Integral 5.3 5.3
5.4 The Fundamental Theorem of Calculus 5.4 5.4
5.5 The Substitution Rule 5.5 5.5
5.6 Using the Calculator to Evaluate Integrals 5.6 5.6
Chapter 5 Test
 Final for Calculus l

## Chapter 6

Integration

Lessons Homework HW Quiz
6.1 Areas Between Curves 6.1 6.1
6.2 Volumes Using Cross-Sections 6.2 6.2
6.3 Volumes Using Cylindrical Shells 6.3 6.3
6.4 Arc Length 6.4 6.4
Chapter 6 Test
 Final for Calculus l