Graphics Reference
In-Depth Information
0as
n
Provethat, for any given
x
,(
R
(
x
))
.
Deduce that
exp(
x
)
x
n
!
.
Use computer graphics to observe the connection between the
graphs of
y
1,
y
1
x
,
y
1
x
x
,..., and
y
exp(
x
).
39 Use Maclaurin's Theorem to say what you can about
R
(
x
) where
x
3!
...
(
1)
x
(2
n
1)!
R
sin
x
x
(
x
).
Provethat, for any given
x
,(
R
(
x
))
0as
n
.
Deduce that
sin
x
x
(2
n
1)!
.
(
1)
Observe the connection between the graphs you drew for qn 16 and
this result.
40 Use Maclaurin's Theorem to say what you can about
R
(
x
).
x
2!
...
(
1)
x
(2
n
)!
R
cos
x
1
(
x
).
Provethat, for any given
x
,(
R
(
x
))
0as
n
.
Deduce that
cos
x
x
(2
n
)!
.
(
1)
Observe the connection between the graphs you drew for qn 16 and
this result.
41 If
f
(
x
)
log(1
x
), useqn 1.8(i) to show that
(
n
1)!
(1
x
)
f
(
x
)
(
1)
.
Use Maclaurin's Theorem to say what you can about
R
(
x
) where
x
2
x
3
x
n
x
)
x
1
R
log(1
...
(
1)
(
x
).