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
Read 1.5 Exponential functions
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
Read 2.3 Calculating Limits.
- 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
Read 2.4 Continuity
- 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
Read 2.5 Limits involving infinity
- 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
Read 2.8 What does f' say about f?
- 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
Read 3.4 The Chain Rule
- 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
Read 3.5 Implicit differentiation
- 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