Graphics Reference
In-Depth Information
Figure6.2
1
-1
1
Figure6.3
17 If (
a
)
1
, taking
,1
a
2 eventually, so [
a
]
1 eventually.
18 Not continuous on Z. Continuous on R
Z.
19 (i), (ii) and (iii) arenull. (iv)
1. For all null sequences (
a
) there is no
singlevalueof
f
(0) for which (
f
(
a
))
f
(0) for continuity.
20 Let
a
berational: (
a
f
(
a
). Let
a
beirrational: ([10
a
]/10
)
a
, but
f
([10
a
]/10
)
1 for all
n
,so
(
f
([10
a
]/10
))
1
0
f
(
a
).
)
a
, but
f
(
a
)
0, so (
f
(
a
))
0
1
21 Let (
a
)
a
.
f
(
a
)
c
,so(
f
(
a
))
c
f
(
a
).
22 Let (
a
)
a
.
f
(
a
)
a
,so(
f
(
a
))
(
a
)
a
f
(
a
).
24 By qn 21,
g
:
x
1 is continuous at every point.
By qn 22,
f
:
x
x
is continuous at every point.
