Graphics Reference
In-Depth Information
41 Usetheidentity
a
x
abx
ac
(
ax
ac
b
to show
that when 0
a
,
c
b
/4
a
ax
bx
c
, for all values of
x
.
Is equality possible? Illustrate on a graph.
b
)
42 If 0
a
, provethat 0
ax
bx
c
, for all values of
x
, if and
only if
b
4
ac
.
If
b
4
ac
, is it possibleto have
ax
bx
c
0?
What is theanalogous claim if
a
0?
The sequence (1
1/
n
)
n
43 Simplify theproduct (
b
a
)(
b
b
a
b
a
...
a
).
Check that your answer will imply 1.3(vi).
Let 0
a
b
.
b
a
b
a
(
n
1)
b
.
Show that (
n
1)
a
44 Usea calculator to find
1
2
,
1
3
,
1
4
,
1
5
1
1
1
to two places of decimals. Denote these numbers by
a
,
a
,
a
and
a
respectively. And in general let
1
n
.
a
1
1
n
and
a
1
1
n
1
45 Put
b
1
in theright-hand inequality of qn 43 to provethat
a
a
(with
thenotation of qn 44). Thus 2
a
, for all
n
.
46 Usea calculator to find
1
2
,
1
3
,
1
4
,
1
5
1
1
1
1
to two places of decimals. Denote these numbers by
b
,
b
,
b
and
b
respectively. And in general let
1
n
.
b
1
47 If (1
1/
n
)(1
1/
x
)
1, provethat
x
n
1.
,
1
n
1
n
Deduce that
b
1
1
1
