Operations with Power Series
Let x = i ens and gcfw_x) = i bur.
1. ex = i nknx"
2. fcfw_x = Z aux
3. x) :I: gm = Z (on :I: sun"
THEOREM 9.22 The Form of a Convergent Power Series
If f is represented by a power series f(x) = 2 an_(x c)" for all x
June 8, 2017
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Department of Mathematics
MATH 3010 SYLLABUS
ELEMENTARY CALCULUS II
Textbook or ebook: Calculus 10th Edition by Larson and Edwards, Cengage Learning Publisher. The
Webassign homework correlates with the section number and topic in the textb
MTH 3010: Calculus II
Course Number: 6507; Section: S1DA
Instructor: Evan Fink
Office/Phone: VC 6-296, (646) 312-4141
Office hours: By appointment; I will be in my office before 1:30 everyday; I intend to arrive at
THEOREM 9.17 Ratio Test
Let 2 an be a series with nonzero terms.
1. The series 2 an converges absolutely when lim Em
2. The series 2 an diverges when lin1 > 1 or lim
. . . . . a
3. The Rano Testis 1nconclus1ve when 11m All = 1.
THEOREM 5.17 Integrals Involving Inverse Trigonometrie
Let u be a differentiable function of x, and let a > 0.
du l u
2. = - arctan- + C
[a2 + u2 a a
du _1 m
3.fumamcsec a +C
THE DISK METHOD
To nd the volume of a solid of r
THEOREM 9.20 Convergence of a Power Series
For a power series centered at c, precisely one of the following is true.
1. The series converges only at c.
2. There exists a real number R > 0 such that the series converges absolutely
Ix cl < R
THEOREM 9.14 Alternating Series Test
Let an > 0. The alternating series
2 ( 1)" an and 2 (1)"+1an
converge when the two conditions listed below are met.
1. lim an = 0
2. an+1 5 an, for alln
THEOREM 9.16 Absolute Convergence
If the series 2'. |
Definitions of nth Taylor Polynomial and nth Maelaurin
If f has n derivatives at c, then the polynomial
eix)= as: +fcfw_tcfw_x c: +flixF a2 +9Lx- a
is called the nth Taylor polynomial for f at e. If e = , then
EILI) =fcfw_' +fcfw_[)x + .thlxg +
Definition of the Area of a Surface of Revolution
Let y = f (x) have a continuous derivative on the interval [a, b]. The area S of the
surface of revolution formed by revolving the graph off about a horizontal or
vertical axis is
S = ZWJ r(x)v l + [f(x)
June 21, 2017
1. a. (5 pts) One of these three functions has an inverse. Circle the one that has an inverse, and explain how you know.
f (x) = 4x3 + x 1, f (x) = 4x3 x + 1, f (x) = 4x3 + x2 9
b. (5 pts) For the corre
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Professor: Cheyne Miller
Classroom: VC - 12 - 170
Baruch email: cheyne dot miller at baruch.cuny.edu
Class meets: MTWTh 5:30pm-8pm
Course Description: Topics to be discussed include: areas, v
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