Hello,
I want to show that
in the interval (0, infinity)
is uniformly continuous using the following definition:
.
My problem is that I want to find something like:
but I've been thinking for a while and I cant find anything.
Hello,
I want to show that
in the interval (0, infinity)
is uniformly continuous using the following definition:
.
My problem is that I want to find something like:
but I've been thinking for a while and I cant find anything.
Two things to notice. may be continuous extended to in the usual (and unique) way. Thus, for any is continuous on and thus by the Heine-Cantor Theorem we see that is unif. cont. on . Thus, any restriction of on is unif. cont., in particular is unif. cont. on . But, ... so try working with that.
If you can use something besides the strict definition and consequences I would note that is unif. cont. on as proven above and is Lipschitz on since it has bounded derivative. From there you can conclude.
Thanks!
I forgot to mention that was given as "indication", so I was trying to find a way to use it and that's what confused me the most. (I still don't see how to use this tho).
Well it might be useful if you're using series to prove this but with this definition :S .