| | |
Summary: MULTIPLE ROOTS
We study two classes of functions for which there is
additional difficulty in calculating their roots. The first
of these are functions in which the desired root has a
multiplicity greater than 1. What does this mean?
Let be a root of the function f(x), and imagine
writing it in the factored form
f(x) = (x - )m
h(x)
with some integer m 1 and some continuous func-
tion h(x) for which h() 6= 0. Then we say that
is a root of f(x) of multiplicity m. For example, the
function
f(x) = ex2
- 1
has x = 0 as a root of multiplicity m = 2. In partic-
ular, define
h(x) =
ex2
- 1
|
