MthT 430 Projects Chapter 1 Inequalities
MthT 430 Projects Chapter 1 Inequalities
This assignment should be typed.
The Triangle Inequality and Applications
For the time being, assume (P1) - (P12), and
|a| =
ì
ï
í
ï
î
a
,
a
³
0
-
a
,
a
£
0
.
The
Triangle Inequality
says that
|a + b|
£
|a| + |b|.
On September 6, 2005, turn in well written solutions of Problems 1-3.
1.
Show that
|
-
b| = |b|.
2.
Show that
|a
-
b|
£
|a| + |b|.
3.
Give examples such that
·
|a
-
b| = |a| + |b|.
·
|a
-
b| < |a| + |b|.
File translated from T
E
X by
T
T
H
, version 3.74.
On 07 Sep 2006, 13:17.