## HW0

Take a few minutes to reflect on your experiences with mathematics. Who were your teachers? What have you learned? What would you like to learn? Write about yourself and your experience with mathematics. To get full credit on this assignment, you must do the following:
• Address each of the three areas (1, 2, 3) below.
• Email your paper (no more than 2 pages) to me by midnight Thursday night with the subject line:
`         MATH1510-[section]  HW0  [last name], [first name] `
1. Your experience with mathematics. Examples of topics you could write about include:
• Compare the best mathematics teacher you ever had with the worst mathematics teacher you ever had. What makes a good math teacher?
• What was the best experience you ever had with mathematics? What was the worst experience?
• What was the hardest math problem you ever attempted? Were you successful? How did you feel about it?
• What do you find easiest about mathematics, and what gives you the most difficulty, and why?
2. The practicality of mathematics. Examples of topics you could write about include:
• Have you ever attempted to solve a math problem just for the fun of it, or do you only do math problems if they are assigned?
• Have you ever done a math problem that had an impact (however small) on your life? If so, describe the impact it had.
• Do you know of any mathematics that has had an impact on your life?
3. Your expectations in this course.
• What do you expect to put into this course, and what would you really like to get out of this Calculus course?
• How do your expectations compare with those of the instructor that are printed in lthe syllabus?
• What do you think would be the most helpful thing that could be done in this course to help you succeed?

## HW1

• Read Section 1.1 Four ways to represent a function

Find the following:

• The definition of a function
• Four different ways to specify a function, and examples of each
• How to identify the domain of a function
• How to identify intervals on which a function is increasing or decreasing
• How to tell if a function is even or odd
• Turn in 1.1 #2, 6, 7, 18, 22, 29, 32, 39, 43, 46, 56, 63, 68
• Extra Credit (3): Write down the name (first and last) and something interesting about 3 students in your section of Calculus, at least one of whom is from a culture different from your own. Indicate which is/are from a different culture.

## HW2

Read 1.2 Mathematical Models: A catalog of essential functions
Find the following:
• How to classify the following families of functions from equations:
• Linear
• Power
• Root
• Polynomial
• Rational
• Trigonometric
• Exponential
• Logarithmic
• Make a scatterplot
• Find an appropriate model for a given data set
• Interpolate values from a model
• Turn in 1.2 #2, 4, 7, 10, 13, 15, 18, 22, 25, 26
• Extra Credit: (10) Find at least two other students currently enrolled in Calculus I with whom you would like to study calculus. Make a single schedule that blocks out the times of all the classes of each student in the group, and select times during the week when you will all meet to study calculus together. Give a place to meet with each block of time. Each person in the group will receive 2 points per block of time.

## HW3

Read 1.3 New Functions from old. Find the following:
• Transformations: Determine the effect on the graph of y = f(x) of each of:
• y = f(x-h) (Subtracting h from the input)
• y = f(x) + k (Adding k to the function values)
• y = af(x) (Multiplying the function values by a)
• y = f(x/b) (Dividing the input by b)
• The definitions of f+g, f-g, f*g, f/g, and f composed with g, and their domains.
• How to break complicated functions down into simple ones.
Turn in 1.3 #2, 4, 8, 20, 21, 29, 41, 42, 50, 51, 53, 59

## HW4

Find the following:

• Learn the laws of exponents
• Limits of exponential functions as x goes to infinity and -infinity
• The definition of Euler's number, e
Turn in 1.5 #3, 4, 5, 9, 13, 19, 21, 26, 30, 31

## HW5

Read 1.6 Inverse functions and logarithms
Find the following:

• Determine whether a function is one-to-one or not.
• Find inverse functions graphically and algebraically
• Learn the laws logarithmic functions
• Solve exponential equations using logarithms and vice versa
Turn in 1.6 #3, 6, 9, 10, 13, 15, 18, 19, 22, 25, 28, 29, 31, 37, 52, 59

## HW6

Read 2.1 The tangent and velocity problems.

• Find the slope of a secant line to a function at 2 points
• Find an average velocity
• Estimate the slope of a curve at a point
• Estimate an instantaneous velocity

Read 2.2 The limit of a function.

• Find one and two sided limits graphically.
• Estimate one and two sided limits numerically.
• Learn the definition of a limit.
• Given a function f, a point a, and a number ε > 0, find the limit L and an appropriate number &delta > 0 so that
|f(x) - L| < ε whenever |x - a|< &delta.
Turn in 2.1 #1, 5, 8, 9
2.2 #1, 5, 8, 15, 19, 30

## HW7

• Use the limit laws to find one and two sided limits.
• Apply the squeeze theorem to find limits.
Turn in 2.3 #1, 2, 7, 8, 16, 19, 25, 27, 41

## HW8

• Learn the definition of continuity of a function at a point.
• Tell when a function is continuous from the left or the right.
• Tell when a function is continuous on an interval.
• Learn the theorems for continuity that follow from the laws of limits.
• Learn which functions are continuous in their domains (Theorem 7)
• Evaluate limits of continuous functions (Theorem 8), and of composite continuous functions (Theorem 9).
• Learn the Intermediate Value theorem (Theorem 9) and apply it to finding the root of a continuous function.
Turn in 2.4 #4, 7, 10, 12, 17, 22, 33, 36, 42

## HW9

• Learn the definition of the limit of f(x) as x approaches infinity.
• Identify horizontal asymptotes
• Learn what it means to say that a limit is infinity
• Identify vertical asymptotes
Turn in 2.5 #1, 4, 8, 15, 22, 28, 39, 40, 51

## HW10

Read 2.6 Derivtives and Rates of Change

• Learn the definition the derivative f'(a).
• Write the equation of the tangent line to a function f at x=a
• Estimate the derivative from a graph.
• Find an instantaneous rate of change
Turn in 2.6 #1, 4, 11, 14, 17, 22, 25, 41, 47

## HW11

Read 2.7 The derivtive as a function

• Learn the definition the derivative f'(x).
• Given a graph of f(x), sketch the graph of f'(x)
• Given an expression for f(x), find a formula for f'(x)
Turn in 2.7 #3, 6, 9, 12, 27, 34, 42, 50, 51

## HW12

• Find how the sign and direction of f' are related to f.
• Find how the sign of f'' is related to f.
• Given a graph of f, find f' and f''.
Turn in 2.8 #3, 7, 8, 9, 19, 23, 28

## HW13

Read 3.1 Derivatives of Polynomial and Exponential Functions

• Learn rules 1, 2, 3, 4, 8, 9 on page 5 of the reference pages
• Write an expression as a polynomial and differentiate
• Differentiate c*e^x.
Turn in 3.1 #3, 6, 9, 12, 15, 18, 21, 25, 28, 45, 48

## HW14

Read 3.2 Product and Quotient rules.

• Learn to product rule for differentiation.
• Learn the quotient rule for differentiation.
Turn in 3.2 #1, 3, 5, 8, 16, 21, 29, 32, 36, 41, 45, 48, 50

## HW15

Read 3.3 Derivatives of trig functions

• Derivatives of basic trig functions: sin(x), cos(x)
• Derivatives of other trig functions: tan(x), sec(x), cot(x), csc(x)
Turn in 3.3 #2, 4, 5, 9, 14, 17, 23, 29, 32, 35, 42, 46

## HW16

• Learn Differentiation Rule #7
• Apply the chain rule to all of functions we have learned so far.
Turn in 3.4 #2, 5, 8, 13, 20, 25, 31, 32, 46, 55, 58, 67, 84

## HW17

• Learn to differentiate implicitly

Read 3.6 Inverse Trig functions and derivatives

• Solve equations of the form trig(x) = a
• Simplify expressions of the form trig(trig^-1(x))
• Learn Differentiation Rules #19-24
Turn in 3.5 #5, 12, 18, 23, 27

Turn in 3.6 #1, 10, 17, 18, 22, 35, 39

## HW18

Read 3.7 Derivatives of logarithmic and exponential functions.

• Learn derivatives of a^x, ln(x), log_a(x)
• Learn the Logarithmic Differentiation technique
Read 4.2 Maximum and minimum values
• Find all critical points of a function.
• Learn the Extreme Value Theorem
• Find absolute extreme values of a function on a closed interval
Turn in 3.7 #2, 3, 5, 10, 11, 27, 36, 37
4.2 #5, 11, 28, 30, 43, 59, 62

Last Update: December 7, 2009
Ronald K. Smith
Graceland University
Lamoni, IA 50140
rsmith@graceland.edu