This discussion is closed.
flyinghorse
Badges: 0
Rep:
?
#1
Report Thread starter 14 years ago
#1
anyone got any ideas for "a continuous function f:[0,1)->R which is bounded but does not attain either of its bounds"?

thanks
0
Jonny W
Badges: 8
Rep:
?
#2
Report 14 years ago
#2
f(x) = x sin(1/(1 - x))

sup f(x) = 1
inf f(x) = -1

But for all x in [0, 1),

|f(x)|
= x |sin(1/(1 - x))|
<= x
< 1
Attached files
0
flyinghorse
Badges: 0
Rep:
?
#3
Report Thread starter 14 years ago
#3
that's great, thanks very much
0
X
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Bristol
    Undergraduate Open Afternoon Undergraduate
    Wed, 23 Oct '19
  • University of Exeter
    Undergraduate Open Day - Penryn Campus Undergraduate
    Wed, 23 Oct '19
  • University of Nottingham
    Mini Open Day Undergraduate
    Wed, 23 Oct '19

Have you made up your mind on your five uni choices?

Yes I know where I'm applying (129)
64.5%
No I haven't decided yet (42)
21%
Yes but I might change my mind (29)
14.5%

Watched Threads

View All