Graphics Reference
In-Depth Information
2
ƒ(
x
) = (
x
+
x
)
Figure6.8
(
g
(
a
)
a
0
g
(
a
), so
g
is not continuous at
a
.
Let
a
be an irrational number then ([10
a
]/10
)
a
. But
g
([10
a
]/10
)
0, so (
g
([10
a
]/10
))
0
a
g
(
a
). So
g
is not
continuous at
a
.
))
(
a
38
x
sin(
x
).
x
(sin
x
)
.
39 See Fig. 6.9.
40 Let (
a
)
a
, then by the continuity of
g
at
a
,(
g
(
a
))
g
(
a
), so by the
continuity of
f
at
g
(
a
), (
f
(
g
(
a
)))
f
(
g
(
a
)).
41 ABS is continuous from qn 32.
42
f
is continuous by qns 41, 23, 26. See Fig. 6.10.
43
f
is continuous by qns 41, 26, 23, 26. See Fig. 6.11.
44 Consider the cases
b
a
and
a
b
separately.
45 max(
f
,
g
)(
x
)
(
f
(
x
)
g
(
x
))
f
(
x
)
g
(
x
)
. Useqns 21, 23, 26, 41.
46 ABS.
47 Maximum domain for
f
r
is R
0
; for
r
f
is R. Both composite
functions are continuous at every point by qns 29, 30 and 40.
48 Qn 19 shows discontinuity at 0. When
x
0, thefunction is sine
r
which is continuous on
R
0
.
50 Maximum domain for
r
. Thecompositefunction is
continuous at every point of its domain, by qns 29, 30, 40.
f
is
R
2, 3
51 Maximum domain for
r
f
is
R
A
, where
A
x
f
(
x
)
0
.
Continuous, by qns 29, 30, 40.
