MAT 271, Summer 2011
Calculus II, Scott Zinzer
6.1 HW
6.1. Velocity and Net Change.
16. A cyclist rides down a long straight rode at a velocity (in m/min) given by v (t) = 400 20t,
for 0 t 10 min.
(a) How far does the cyclist travel in the rst 5 min?
(b)
1
4/26/16
10.1
Example 1. For the curve given by the parametric equations:
x = t2 + 2, y = 4t,
4 t 4
(a) make a table of values
(b) plot the points
(c) identify the curve
(d) eliminate the parameter
c
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Contents
1
Aug 28
2
2
Sep 4
6
3
Sep 11
9
4
Sep 18
13
5
Sep 25
16
6
Oct 2
19
7
Oct 9
22
8
Oct 23
25
9
Oct 30
28
10 Nov 6
30
11 Nov 13
33
1. Aug 28
section 7.1, problems 1, 3, 5.
1. Integration by parts
e2 sin(6) d.
Soln : First let t = 2. Then we have
dt =
Exam 2 Review (6.16.6)
The following review practice problems are meant to help you focus your study for the exam. They
are not test sample problems.
1. A projectile is launched vertically from the 5. Find the volume of solid generated by rotating
ground
Taylor and MacLaurin Series
Taylor and MacLaurin Series
Suppose the function f has derivatives f (k)(a) of all orders at the point a
If we write the Taylor polynomial of degree n for f centered at a and allow n to
increase indefinitely, a power series is
Sequences
Sequences
A sequence is an ordered list of numbers. Each number in the
sequence is called a term of the sequence.
cfw_a1, a2 , a3 ,
, an ,
Alternate notations:
cfw_an
cfw_an n1
or
The subscript n which appears in an is called the index. The ch
Series
Series
A series is a sum of an infinite set of numbers.
a1 a2 a3
ak
k 1
How is it possible to sum an infinite set of numbers and produce a finite
sum?
Consider the following example:
Imagine you are eating a pie.
S1
You first eat half of the pie
The Divergence and Integral Test
Divergence Test
The Divergence Test: If lim an 0 then the series
n
a
n 1
n
diverges.
NOTE: If lim an 0 , the Divergence Test is inconclusive, that is, the
n
series might converge or it might diverge.
Example:
Determine w
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MAT 271
Test Concepts
End Concepts
mostly 10.1-10.3
Terri L. Miller
Spring 2016
revised April 28, 2016
What you should be able to do.
series
comparison test
limit comparison test
integral test
parametric equations
parameter
parametric curve
orient
MAT 271
Test Concepts
Final Concepts
7.7-10.2
Terri L. Miller
Spring 2016
revised April 30, 2016
What you should be able to do.
Know how and when to use integration techniques
substitution
symmetric functions
integration
by parts Z
Z
udv = uv
vdu
tri
MAT 271
Series Worksheet 3
Terri L. Miller
Spring 2016
revised April 21, 2016
(1) Determine whether the series is divergent or convergent. If it is convergent, evaluate
its sum.
X
22(n+1)
(a)
4n+1
n=0
X
4n
(b)
This is NOT the type on test 3; best with com
this green sheet was distributed; you were to leave the bottom part with me before leaving
MAT 271 Day 2 Class #17165 January 14, 2016
Reminders:
You will find your syllabus and other course information via my web page:
https:/math.la.asu.edu/terri
and th
MAT 271
Test Concepts
Exam 2
7.8, 6.16.5, 6.7, 8.18.2
Terri L. Miller
Spring 2016
revised March 21, 2016
What you should be able to do.
improper integrals
infinite limit
discontinuity at endpoint
discontinuity at interior point
more than one disconti
Left as an exercise: solution on next page
11
ADDENDUM
Example 15. Use the ratio test to decide if the series converges or
diverges:
1
X
(2n + 3)!
.
2
(n!)
n=1
an+1 (2(n + 1) + 3)!
(n!)2
(2n + 2 + 3)!
(n!)2
=
=
an
(n + 1)!)2|
(2n + 3)!
(n + 1)!)2 (2n + 3)
MAT 271 FIRST DAY JANUARY 12, 2016
TERRI L. MILLER
Attendance Policies:
roll called (second part of attendance for day 1) while you were grading your quiz
0
if not on roll, you were to see me
item attendance is taken
maximum number of classes that can
MAT 271
Test Concepts
Exam 1
7.1 7.7
Terri L. Miller
Fall 2015
revised February 10, 2016
What you should be able to do.
Know how and when to use integration techniques
substitution
symmetric functions
integration
by partsR
R
udv = uv vdu
trigonometr
Renee Crudup
Assignment Section 7.5 due 09/21/2014 at 11:30pm MST
Vaz MAT 271 Fall 2014
Correct Answers:
1. (1 pt) Use the table of in Integrals in the back of your
textbook to evaluate the integral:
(1/(2*3)*(sec(3*x)*tan(3*x)+ln(abs(sec(3*x)+tan(3*x)
4
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