MATH 2A SUGGESTED HOMEWORK PROBLEMS
UC IRVINE, ACADEMIC YEAR 201617
STEWART, SINGLE VARIABLE CALCULUS: EARLY TRANSCENDENTALS
EIGHTH EDITION
These suggested problems correspond to the eighth edition. They also correspond to the eighth edition
of the UC Ir
Syllabus: Math 2A Calculus class 44240 (Lec C), Winter 2017
Text: Calculus: Early Transcendentals (8th Edition) by James Stewart
Lectures: Mon, Wed, Fri, 4pm  4:50pm, HG 1800
Instructor: Vladimir Goren, vgoren@math.uci.edu
FINAL EXAM: March 18, Saturday,
Overview of the WebWork homework system
WebWork is an Internetbased system for generating and delivering homework type
problems to students. Its goal is to support instruction and textbased assigned homework
problems and has been an important part o
Math 2B
Class 28
06/01/16
Taylor series and Maclaurin series
Remember last class when we had some functions that we were able to write as power series because they
looked like a geometric series? Taylor Series and Maclaurin Series enable us to turn every
2.2  The Limit of a Function
Last edited on October 15th , 2014
1
Limits
Definition: Suppose that f is defined near the number a (except
possibly at a itself). Then we write
lim f (x) = L
xa
and say that the limit of f (x) exists and equals L, if we can
2.3 Addendum  Infinite limits
Last edited on April 16th , 2015
Here we briefly go over limits that go to or as x a. These will be limits of the form
n
,
0
where n 6= 0.
1
First example: factoring
Find
x3 10x2 + 9x
x1
x2 + x 2
lim
Solution: First, note th
Guide to Derivatives
November 14, 2014
Part I
Derivative Rules
1
Algebra with derivatives
Derivatives distribute over sums and differences:
d
d
d
[f (x) + g(x)] =
f (x) +
g(x)
dx
dx
dx
and
d
d
d
[f (x) g(x)] =
f (x)
g(x)
dx
dx
dx
Derivatives do not distr
2.8  The Derivative as a Function
Last edited on April 16th , 2015
Here we talk in more detail about the derivative and its properties.
1
The derivative as a function
0
In the previous section we were looking at f (a), that is, the derivative of f evalua
1.5  Exponential Functions
Last edited on October 5th , 2014
In this section we will look at exponential functions, that is, functions of
the form f (x) = bx where b is some constant base greater than 0. Exponential
functions are used to model population
1.6  Inverse Functions and Logarithms
Last edited on October 12th , 2014
In this section we will first learn about inverse functions. We will then
introduce logarithms, which are the inverses of exponential functions. We will
also discuss inverse trigono
2.1  The Tangent & Velocity Problems
Last edited on October 12th , 2014
1
Tangent lines
Let us introduce this section by working through an example. We would like
to find the equation of the line tangent to the curve of f (x) = x2 at the point
P = (1, 1)
2.6  Limits at Innity & Horizontal
Asymptotes
th
Last edited on October 26
, 2014
In this section we will learn how to calculate limits of functions as
or
x ,
x
and we will look at what eect this can have on a graph.
1 Limits at innity
Denition:
Let
some
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Ab Wilt hows mm)
5 MP; 90 +0 Mm
TWM denier
R" 5"? 93 694
um. 01:00qu
F 0" 5:00
Mt: Wm Fmigluei
Ue0;+;on. A 9M0" F 9 M _,
MMMWHVC of 5" 0" 0n Warm] I
is 9" all x in I. 61. Find Me ahderi'mve. o? 96:); max
(i161 n! m Sham whose.
2.7  Derivatives & Rates of Change
Last edited on April 16th , 2015
In this section we will formally introduce the concept of a derivative, and look at several examples.
1
The tangent problem
Recall that in section 2.1 we were looking at the tangent line
4.3  How derivatives affect the shape of a graph
December 2, 2014
In this section well briefly discuss the first and second derivatives, and how they affect graphs of functions.
1
Increasing and decreasing on an interval
0
0
Critical numbers are xvalues
2.3  Calculating Limits Using Limit Laws
Last edited on October 12th , 2014
In this section we will learn how to calculate limits of functions using a number of different limit laws.
1
Basic limit laws
First well go over the most basic limit laws, which
4.4  Indeterminate forms & LHopitals rule
May 21, 2015
1. Today were getting back to limits for a little bit.
(a) Remember weve run across limits of the form
p
lim x2 + 3 x =
x
and
n
1
= 1 (= e in this case)
1+
n
n
lim
and I called them indeterminate. T
3.1 Dervivaiives of pol momials
and cfw_XfoVHHHal func'lziomi
Fumcciom DevlvaLive
C O
7\ 1
1
K
3
X
X
1 . 4
<'T Powev RuLe The dewivative 0'? a poL/inomial: x) 1, (16>0)
. (mmHz)
0 6 h
v. "
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331 h
h K
b"b " 1>
3 m_
cfw_1. \n
A M
_ In
Recatl tha the olewivative oY a umc3ciom 19
a: a. number a is:
Hmm  Had
WW. 2.9 The clearWakive a5 a FMmCtl'OV'I
We ConsMedea! Hm? derrivaiive 0? a Pumciiom 7P
ad. a. 436de number a :
Na) = m WNW)  Ha)
Irv>0 '1
Now we Lei; the numbev a vow3,
We rep
Secdon 27 EXEvcise 4'5,
1: a. ball is ihrvoww 31440 the aid wiLk a xialum? or 40 5/5)
Z'LS helht (in (leek) an t SQConaIS is given b3 H=q0t'46t1.
Find the melon? when i = 2.
The VL0LL 13 (m; the mscantaneuus veto Lila) V (4:)
al; LEVI/IE t :2 [5
2
MATH 2A SUGGESTED HOMEWORK PROBLEMS
UC IRVINE, ACADEMIC YEAR 201617
STEWART, SINGLE VARIABLE CALCULUS: EARLY TRANSCENDENTALS
EIGHTH EDITION
These suggested problems correspond to the eighth edition. They also correspond to the eighth edition
of the UC Ir
Sechow 2.5 Exewusc 45?.
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