Test 2 Key Concepts:
Newtons Method 4.8
If given a function, f(x) use:
x(n+1)=xn- (f(xn) / f(xn)
Eulers Method 9.2
If given the initial value : y=F(x,y), y(x0)=y0, step-size, h, use:
Yn=yn-1+hF(xn
Integration and Approximation
Test 2
Closed book and notes. No calculators or any other electric device. Show your work!
problem points score
1
10
2
10
3
10
4
10
5
20
6
20
7
20
total
100
Name:
Andrew ID:
Section:
1
2
1. (10 points) Determine an explicit s
Convergence of series
The p-series.
1
np
is convergent if p > 1 and divergent if p 1.
a rn1 is convergent if |r| < 1 and divergent if |r| 1.
The geometric series.
Test for Divergence. If limn an = 0 or the limit does not exist, then
an is divergent.
The I
Assignment 5
Due on Thursday, February 25, 2016, before recitation
This assignment includes 10 problems, 100 points in total. Please rst read
section 9.1 and 9.3 in textbook and then complete this assignment. Be sure to
provide necessary details of comput
Assignment 8
Due on Thursday, March 31, 2016, before recitation
This assignment includes 10 problems, 100 points in total. Please first read
section 10.3 and 12.1 in textbook and then complete this assignment. Be sure
to provide necessary details of compu
Assignment 2
Due on Thursday, January 28, 2016, before recitation
This assignment includes 10 problems, 100 points in total. Please first read
section 7.3 in textbook and then complete this assignment. Be sure to provide
necessary details of computation a
Assignment 10
Due on Thursday, April 28, 2016, before recitation
This assignment includes 10 problems, 100 points in total. Please first read
section 11.1, 11.2, 11.4, 11.8 and 11.9 in textbook and then complete this assignment. Be sure to provide necessa
Assignment 6
Due on Thursday, March 17, 2016, before recitation
This assignment includes 10 problems, 100 points in total. Please first read
section 10.1 and 10.2 in textbook and then complete this assignment. Be sure
to provide necessary details of compu
Assignment 4
Due on Thursday, February 18, 2016, before recitation
This assignment includes 10 problems, 100 points in total. Please rst read
section 7.8, 8.1, 9.1, 9.2 and 9.3 in textbook and then complete this assignment.
Be sure to provide necessary de
Assignment 1
Due on Thursday, January 21, 2016, before recitation
This assignment includes 10 problems, 100 points in total. Please rst read
Section 7.2 in textbook and then complete this assignment. Be sure to provide
necessary details of computation and
Assignment 9
Due on Thursday, April 21, 2016, before recitation
This assignment includes 14 problems, 100 points in total. Please first read
Chapter 11 and Chapter 12 in textbook and then complete this assignment. Be
sure to provide necessary details of c
Assignment 7
Due on Thursday, March 24, 2016, before recitation
This assignment includes 10 problems, 100 points in total. Please first read
section 10.2 and 10.3 in textbook and then complete this assignment. Be sure
to provide necessary details of compu
Integration and Approximation
Test 3
Closed book and notes. No calculators or any other electric device. Show your work!
problem points score
1
20
2
10
3
15
4
15
5
25
6
15
total
100
Name:
Andrew ID:
Section:
Taylor Series:
1
=
1x
x
e =
n=0
(1)n
sin x =
n=
gear
Name -_____1___m___1____i____i__1____i____1___
Department of Mathematical Sciences
CARNEGIE MELLON UNIVERSITY
21122 Integration, Different
Test 3: April 22, 2014
ial Equations, and Approximation
E TuTh 8:30 PH DH 1211 Chu,
F TuTh 10:30 PH 125C
Assignment 3
Due on Thursday, February 4, 2016, before recitation
This assignment includes 10 problems, 100 points in total. Please first read
section 7.4 in textbook and then complete this assignment. Be sure to provide
necessary details of computation a
Summary for test1
1. Integration Formula (constants are omitted)
xn dx =
xn+1
n+1
(n = 1)
ex dx = ex
1
dx = ln |x|
x
sin x dx = cos x
sec2 x dx = tan x
cos x dx = sin x
csc2 x dx = cot x
sec x tan x dx = sec x
csc x cot x dx = csc x
sec x dx = ln | sec x