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 by
mtan = lim
ba
f (b) - f (a) b-a
and given a positio
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 the area of a polygon by cutting it up into triangles an
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 Approximation
We will now develop a method of linearizing (turni
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 car in mph as a function of time was given by
v(t) = 30
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 ideas we will spend chapters 2-4 on.
1.1
Motion
Denition 1
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. It the function has no inverse function, explain why. 1
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 function the values have a constant dierence. Solution: We c
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(x) = Solution: 1 +1x x 1 f g = +1x x 1 1 f g = (1 x) =
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. Solution: The period of the rotation of the moon around t
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 will need a four function calculator to solve one of the p
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 Solution: Since the slope of the line is -1, the slope-interc
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 interval (open, closed, innite)? Solution: The union of any tw
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 paper for each question. Easy Questions: 1. (5 pts) Find th