Precalculus
Version = 3, Corrected Edition
by
Carl Stitz, Ph.D.
Lakeland Community College
Jeff Zeager, Ph.D.
Lorain County Community College
July 4, 2013
ii
Acknowledgements
While the cover of this textbook lists only two names, the book as it stands tod
Fall Term, 2014
MA100 - B & C - Introductory Calculus for the Natural Sciences
Instructor:
Oce:
Oce Hours:
Dr. Fei Xu
BA303E
MW 11:30 am-12:20 pm in BA535 (Bricker Academic Building),
other times by appointment.
Email: [email protected], Include course number or
MA100 Recommended Problems
Precalculus Problems
Resources: There are 3 sources for the problems, all freely available on the internet. It is
recommended you download and save all the les, in case the websites become unavailable at some
future date.
1. Ste
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YES
NO
MA100 Lab Report 1 - Algebra Review
Name:
Student Number:
Winter 2017
1. [6 marks] Solve the following equation for x. Where appropriate, state your answers in interval or set notation.
(a) 2 x + 3 = 1
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YES
NO
MA100 Lab Report 4 - Inverse Functions; Logarithmic Functions; Lines
Name:
Student Number:
Winter 2017
1. [3 marks] Determine the domain, range and the inverse of f (x) = x7/4 and verify your result by c
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YES
NO
MA100 Lab Report 2 - Functions
Name:
Student Number:
Winter 2017
1. [3 marks] Given that x = 1 is a root of f (x) = x3 4x2 + 5x 2, use long division of polynomials to fully factor f (x).
x2 3x + 2
x1
x3
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YES
NO
MA100 Lab Report 4 - Inverse Functions; Logarithmic Functions; Lines
Name:
Student Number:
1. [2 marks] Sketch y = 2x and y = 0.5x on the axis below. Be sure to label your graph.
2. [8 marks] Solve the f
MA 100 Introductory Calculus for the Natural Sciences
1
Precalculus Problems
Fall 2015
Resources: There are 4 sources for the problems, all freely available on the internet. It is recommended
you download and save all the les, in case the websites become
Beginning and Intermediate Algebra
Student Solutions Manual
Complete worked solutions to odd problems
Solutions manual has not been cross checked for accuracy.
If you disagree with this solutions manual you should check with your instructor.
Should you f
Fall Term, 2015
MATHEMATICS 100 - Introductory Calculus for the Life Sciences
Instructor: Dr. Cristina Stoica
E-mail: [email protected]
Oce: BA529
Oce Hours: Monday, Wednesday 10:00am -11:00am and 1:00pm - 2:00pm, or by
appointment.
Lectures (Section A): Mon
MA110 Lab Report 2
Name:
Student Number:
Lab:
Fall 2015
1. [4 marks] A sports car is purchased and depreciates linearly in value.
(a) If the value of the car is $43500 after four years and $24000 after seven years, express the value of the car V as a line
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NO
MA100 Lab 2 - Analytic Geometry and Intro to Functions
Name:
Student Number:
Lab
Fall 2015
1. [2 marks] Determine the equation of the line (in slope-intercept form) passing through the points (1, 5) and
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YES
NO
MA100 Lab 1 - Algebra Review
Name:
Student Number:
Lab
Fall 2015
1. [5 marks] Fully factor each of the following polynomials.
(a) x4 + 4x3 12x2
(b) 6x2 13x + 6
x4 + 4x3 12x2 = x2 (x2 + 4x 12)
two numbers
MA100 Lab Notes - Analytic Geometry; Intro to Functions and their Graphs
Text References: Stewart Analytic Geometry, and sections 1.3 - 1.6 from Stitz-Zeager
Linear Functions:
A straight line passing through a point (x1 , y1 ) and has slope given by m has
MA100 Lab Notes - Transformations, Composition and Function Operations, Inverses
Text References: Precalc text - 1.5, 1.7, 5.1-5.2
Transformations and Translations
Consider the graph of the function f (x). Then, if c > 0,
f (x) c
is the graph of f shifted
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YES
NO
MA100 Lab 3 - Functions Continued
Name:
Student Number:
Lab
Fall 2015
1. [8 marks] Sketch the following graphs by applying transformations to the base functions.
1
(a) 2 1 x 2
(b) |2x 1| 2
4
(c)
2
+1
2x
MA101 Lab 10 Report - Improper Integrals
Name:
Student Number:
Lab
Winter 2015
1. [12 marks] Determine whether each integral is convergent or divergent. If the integral is convergent, compute
its value. Show your work.
Z
ln(x)
(a)
dx
x
1
Z
ZN
ln(x)
dx
x
=
MA101 Lab 6 Report - Antiderivatives; FTOC
Name:
Student Number:
Lab
Winter 2015
1. [3 marks] Suppose that the growth rate of a population at time t undergoes seasonal fluctuations according to
dN
= 3 cos(2t)
dt
1
where t is measured in years and N (t)
MA101 Lab 4 Report - LH
ospitals Rule; Trig Limits
Name:
Student Number:
Lab
Winter 2015
1. [11 marks] Evaluate the following limits. Indicate all indeterminate forms encountered and the points at which
lHospitals rule is applied. Justify your answers by
MA101 Lab 11 Report - Differential Equations
Name:
Student Number:
Lab
Winter 2015
1. [10 marks] Let L(t) denote the length (in inches) of a certain fish at time t (in months), and assume that this
fish grows according to the von Bertalanffy equations
dL
MA101 Lab 5 Report - Linear Approximations; The Taylor Approximation
Name:
Student Number:
Lab
Winter 2015
1. [5 marks] Find the linearization
of the
function f (x) = 3 1 + x at a = 0. Use the linear approximation of f
3
3
to estimate the numbers 0.95 and
MA101 Lab 3 - IVT; MVT; Sandwich Theorem
Name:
Student Number:
Lab
Winter 2015
1. [4 marks] Consider f (x) = cos(2x) + 2 sin2 x 3x + 4.
Determine whether the Intermediate Value Theorem can be used to find a root (f (x) = 0) in each of the
following interv
MA101/103 Week 1 - Maple Tutorial
Name:
Lab:
Spring 2013
This worksheet is designed to familiarize you with Maple and some of its common commands. These commands, as
well as many others (which will be shown to you in upcoming labs), will be used throughou
MA101 Lab 7 Report - Applications of Integration; Substitution
Name:
Student Number:
Z
1. [5 marks] Consider the integral w =
Lab
Winter 2015
p
2x(x2 ) x2 + 1dx.
(a) Load the student package in Maple and define the above integral as follows:
with(student)