Suppose that ϕ ( h ) is an approximation to some quantity M for every h > 0 and that M = ϕ ( h ) + a 2 h^ 2 + a 4 h^4 + a 6 h^ 6 + . . . for some constants a 2 , a 4 , a 6 , . . . Use the values ϕ ( h ), ϕ ( h/ 3 ) and ϕ ( h/ 9 ) to produce an O ( h^ 6 ) approximation to M . .

1. Suppose that
ϕ
(
h
) is an approximation to some quantity
M
for every
h >
0
and that
M
=
ϕ
(
h
) +
a
2
h^
2
+
a
4
h^4
+
a
6
h^
6
+
. . .
for some constants
a
2
, a

2. 4
, a
6
, . . .
Use the values
ϕ
(
h
),
ϕ
(
h/
3
) and
ϕ
(
h/
9
) to produce an
O
(
h^
6
)
approximation to
M
.