Graphics Reference
In-Depth Information
s
(2
x
)
2
2
2
s
(
x
)
s
(
x
)
.
(vii)
s
is linear on intervals [
m
/2, (
m
1)/2] for any integer
m
.
is linear on intervals [
m
/4, (
m
s
1)/4] for any integer
m
.
,(
m
s
is linear on intervals [
m
/2
1)/2
] for any integer
m
.
(viii)
s
(1/3)
1/3.
s
(1/3)
(1/2
)
s
(2
/3)
1/(2
/3).
b
(1/3)
1/3
(1/3)(1/2)
(1/3)(1/4)
...
(ix)
b
(
c
)
L
(
c
) and
b
(
d
)
L
(
d
) from (vii).
b
(
k
)
L
(
k
)
(1/2
)
b
(2
(
m
1/3)/2
)
L
(
k
)
(1/2
)
b
(1/3). Now use
(viii).
(x) Consider
b
(
k
)
b
(
a
)
b
(
c
)
b
(
a
)
L
(
k
)
L
a
L
(
a
)
(
c
)
L
(
a
)
a
k
c
a
k
c
a
b
(
k
)
L
(
k
)
1
1
(
b
(
a
)
L
(
a
))
a
.
k
a
c
k
a
Also, 0
k
a
(1
1/3)/2
.
(xi) Like(x).
(xii) Every neighbourhood of
a
contains an interval of the form
(
a
,
a
] and therefore points corresponding to
c
,
k
and
d
as in
(ix), (x) and (xi). So there can be no limit
g
such that
1/2
b
(
x
)
b
(
a
)
1
5
,
a
g
x
for all
x
inside
any
neighbourhood of
a
.
