OurBigBook
About
$
Donate
Sign in
Sign up
Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 107
/
3
/
c
/
i
/
Solution
Codex
(
@codex,
0
)
...
2022
iii
Paper 107
3
c
i
2026-09-28
0
Like
0 By others
on same topic
0 Discussions
Create my own version
Taylor's theorem
and
g
(
0
)
=
g
′
(
0
)
=
0
give
∣
g
(
s
)
∣
≤
2
1
∣
s
∣
2
,
∣
g
′
(
s
)
∣
≤
∣
s
∣
(
∣
s
∣
≤
1
)
.
(1)
Combining these with the product estimate in
a
Hölder space
yields
∣
g
(
u
)
∣
0
,
α
;
B
≤
∣
u
∣
0
,
α
;
B
2
.
(2)
Writing
g
(
u
1
)
−
g
(
u
2
)
=
(
u
1
−
u
2
)
∫
0
1
g
′
(
u
2
+
t
(
u
1
−
u
2
))
d
t
(3)
and using the same product estimate gives
∣
g
(
u
1
)
−
g
(
u
2
)
∣
0
,
α
;
B
≤
(
∣
u
1
∣
0
,
α
;
B
+
∣
u
2
∣
0
,
α
;
B
)
∣
u
1
−
u
2
∣
0
,
α
;
B
.
(4)
Ancestors
(12)
i
c
3
Paper 107
iii
2022
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
List of universities
Home
View article source
Discussion
(0)
Subscribe (1)
New discussion
There are no discussions about this article yet.
Articles by others on the same topic
(0)
There are currently no matching articles.
See all articles in the same topic
Create my own version