Chapter 3 Notes
The Derivative
We now discuss the idea of a derivative which is fundamental to calculus.
1
The Definition
Recall that the slope of the tangent line to a curve f (x) at x = a is defined
Chapter 6 Notes
The Definite Integral
1
1.1
Area
What is Area?
Definiton 1. A region is a set of points in a plane and a polygonal region is a polygon, together with its interior. We can always find t
Chapter 4 Notes
Derivative Applications
The derivative is the basis of most of advanced mathematics. We will see a few of its simplest applications in this chapter.
1
Local Linearization and Approxima
Chapter 1 Notes
Real Functions
Functions are powerful tools for understanding and predicting the time evolution of physical systems. Example 1. Suppose that you discovered that the velocity of a race
Chapter 2 Notes
Limits and Continuity
1
Rates of Change and Tangent Lines
We now consider the important idea of a tangent line to a curve. This is the foundation for the limiting and dierentiation ide
Calculus Solutions: Chapter 1.7
Aaron Peterson, Stephen Taylor September 6, 2006
Write a formula for each of the following function descriptions. Then describe its inverse and write a formula for it.
Calculus Solutions: Chapter 1.4
Aaron Peterson, Stephen Taylor February 12, 2006
2. Show that in a regular table for an exponential function, the values have a constant ratio, while for a linear funct
Calculus Solutions: Chapter 1.6
Aaron Peterson, Stephen Taylor September 6, 2006
Find formulas for f + g, f g, f g, f /g, g f , and f g for each of the following pairs of functions. 1b. f (x) = 1 x, g
Calculus Solutions: Chapter 1.5
Aaron Peterson, Stephen Taylor September 6, 2006
Give the period of each of the following familiar periodic phenomena: 1b. the rotation of the moon around the earth. So
Math 112 Exam 2
Stephen Taylor Section 12
Instructions: Answer all questions. Work on scratch paper will not be graded under any circumstance. You may write on the back if you need more space. You wil
Calculus Solutions: Chapter 1.3
Aaron Peterson, Stephen Taylor September 6, 2006
Give equations in slope-intercept form for the lines determined as follows: 2b. on point (1,4) and with slope -1 Soluti
Calculus Solutions: Chapter 1.1
Aaron Peterson, Stephen Taylor December 21, 2005
1. Under what conditions is the union of two intervals another interval? Does your answer depend on the type of interva
Math 112 Exam 1
Stephen Taylor Section 12
Answer the following to the best of your ability. Leave all answers in exact form (do not try to compute decimal approximations). Use a separate sheet of pape