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MAT 1330, Fall 2010 Assignment 6
Due Wednesday November 24, at the beginning of class.
Late assignments will not be accepted; nor will unstapled assignments.
Instructor (circle one): Frithjof Lutscher
Angelika Welte
Aziz Khanchi
Robert Smith?
DGD (circle one): 1
2
3
4
Student Name
Student Number
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Question 1.
Consider the function
f
(
x
)=
x
(
x
+ 1)(
x
+ 2)(
x
+ 3) which is de±ned for all
x
in
R
. Show that the equation
f
!
(
x
) = 0 has three distinct solutions. Answer:
The function
f
(
x
) is continuous and di²erentiable on
R
.
Furthermore,
f
(0) =
f
(
−
1) =
f
(
−
2) =
f
(
−
3) = 0
.
Therefore, according to Rolle’s theorem:
There is some
α
∈
(
−
3;
−
2) such that
f
!
(
α
)=0.
There is some
β
∈
(
−
2;
−
1) such that
f
!
(
β
There is some
γ
∈
(
−
1; 0) such that
f
!
(
γ
.
Question 2.
Use Newton’s method to approximate a solution of the equation
2 cos(
x
)
−
x
=0
.
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This note was uploaded on 09/17/2011 for the course MAT 1330 taught by Professor Dumitriscu during the Fall '08 term at University of Ottawa.
 Fall '08
 DUMITRISCU

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