Is $sqrt{x^3}$ uniformly continuous?
up vote
1
down vote
favorite
$f(x) = sqrt{x^3}, x in (2,3)$ and $ g(x) = x^3, x in Bbb R$.
I have showed that $g$ is not uniformly continuous, but unable to do the 1st one i.e. $f(x) = sqrt{x^3}, x in (2,3)$.
Need some help for that part!
real-analysis continuity
asked Nov 17 at 11:31
user8795
5,57961846
add a comment |
up vote
1
down vote
favorite
$f(x) = sqrt{x^3}, x in (2,3)$ and $ g(x) = x^3, x in Bbb R$.
I have showed that $g$ is not uniformly continuous, but unable to do the 1st one i.e. $f(x) = sqrt{x^3}, x in (2,3)$.
Need some help for that part!
real-analysis continuity
asked Nov 17 at 11:31
user8795
5,57961846
Do you know differentiation / the mean value theorem? That will be helpful.
– астон вілла олоф мэллбэрг
Nov 17 at 11:37
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
$f(x) = sqrt{x^3}, x in (2,3)$ and $ g(x) = x^3, x in Bbb R$.
I have showed that $g$ is not uniformly continuous, but unable to do the 1st one i.e. $f(x) = sqrt{x^3}, x in (2,3)$.
Need some help for that part!
real-analysis continuity
asked Nov 17 at 11:31
user8795
5,57961846
$f(x) = sqrt{x^3}, x in (2,3)$ and $ g(x) = x^3, x in Bbb R$.
I have showed that $g$ is not uniformly continuous, but unable to do the 1st one i.e. $f(x) = sqrt{x^3}, x in (2,3)$.
Need some help for that part!
real-analysis continuity
real-analysis continuity
asked Nov 17 at 11:31
user8795
5,57961846
asked Nov 17 at 11:31
user8795
5,57961846
asked Nov 17 at 11:31
user8795
5,57961846
asked Nov 17 at 11:31
user8795
5,57961846
asked Nov 17 at 11:31
user8795
5,57961846
5,57961846
Do you know differentiation / the mean value theorem? That will be helpful.
– астон вілла олоф мэллбэрг
Nov 17 at 11:37
add a comment |
Do you know differentiation / the mean value theorem? That will be helpful.
– астон вілла олоф мэллбэрг
Nov 17 at 11:37
Do you know differentiation / the mean value theorem? That will be helpful.
– астон вілла олоф мэллбэрг
Nov 17 at 11:37
Do you know differentiation / the mean value theorem? That will be helpful.
– астон вілла олоф мэллбэрг
Nov 17 at 11:37
add a comment |
2 Answers
2
active
oldest
votes
up vote
4
down vote
accepted
$f$ (same formula) is continuous on $[2,3]$ hence uniformly continuous on it (by compactness of $[2,3]$) and its subspaces (by definition uniform continuity inherits to subspaces).
answered Nov 17 at 11:37
Henno Brandsma
102k344108
add a comment |
up vote
1
down vote
Hint. Any function which is continuous in a compact set is also uniformly continuous there and in any of its subsets.
answered Nov 17 at 11:39
Robert Z
91.1k1058129
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
accepted
$f$ (same formula) is continuous on $[2,3]$ hence uniformly continuous on it (by compactness of $[2,3]$) and its subspaces (by definition uniform continuity inherits to subspaces).
answered Nov 17 at 11:37
Henno Brandsma
102k344108
add a comment |
up vote
4
down vote
accepted
$f$ (same formula) is continuous on $[2,3]$ hence uniformly continuous on it (by compactness of $[2,3]$) and its subspaces (by definition uniform continuity inherits to subspaces).
answered Nov 17 at 11:37
Henno Brandsma
102k344108
add a comment |
up vote
4
down vote
accepted
up vote
4
down vote
accepted
$f$ (same formula) is continuous on $[2,3]$ hence uniformly continuous on it (by compactness of $[2,3]$) and its subspaces (by definition uniform continuity inherits to subspaces).
answered Nov 17 at 11:37
Henno Brandsma
102k344108
$f$ (same formula) is continuous on $[2,3]$ hence uniformly continuous on it (by compactness of $[2,3]$) and its subspaces (by definition uniform continuity inherits to subspaces).
answered Nov 17 at 11:37
Henno Brandsma
102k344108
answered Nov 17 at 11:37
Henno Brandsma
102k344108
answered Nov 17 at 11:37
Henno Brandsma
102k344108
answered Nov 17 at 11:37
Henno Brandsma
102k344108
102k344108
add a comment |
add a comment |
up vote
1
down vote
Hint. Any function which is continuous in a compact set is also uniformly continuous there and in any of its subsets.
answered Nov 17 at 11:39
Robert Z
91.1k1058129
add a comment |
up vote
1
down vote
Hint. Any function which is continuous in a compact set is also uniformly continuous there and in any of its subsets.
answered Nov 17 at 11:39
Robert Z
91.1k1058129
add a comment |
up vote
1
down vote
up vote
1
down vote
Hint. Any function which is continuous in a compact set is also uniformly continuous there and in any of its subsets.
answered Nov 17 at 11:39
Robert Z
91.1k1058129
Hint. Any function which is continuous in a compact set is also uniformly continuous there and in any of its subsets.
answered Nov 17 at 11:39
Robert Z
91.1k1058129
edited Nov 17 at 13:31
answered Nov 17 at 11:39
Robert Z
91.1k1058129
answered Nov 17 at 11:39
Robert Z
91.1k1058129
answered Nov 17 at 11:39
Robert Z
91.1k1058129
91.1k1058129
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3002242%2fis-sqrtx3-uniformly-continuous%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Do you know differentiation / the mean value theorem? That will be helpful.
– астон вілла олоф мэллбэрг
Nov 17 at 11:37