6 дек. 2013 г. · One such example is f(x)=sin(x). Here is how I found this example: The property of uniformly continuous means that the function has a maximal ...

1 нояб. 2013 г. · Intuitively uniform continuity means your function can't get infinitely steeper on (a,b) the way 1/x does on (0,1). Steepness doesn't only mean ...

30 апр. 2016 г. · A uniformly continuous function is that it doesn't accelerate without bound and then stay there as the function itself increases (or decreases) without bound.

12 мая 2017 г. · You can take f(x)=x, it is uniformly continuous but does not have bounded variation over R. Even you can find uniformly continuous functions without bounded ...

15 нояб. 2014 г. · Uniform continous functions transform Cauchy sequences into Cauchy sequences. This function transform the Cauchy sequence un=1/n ...

3 июн. 2016 г. · To give a one-variable example, the function x2 viewed R→R is not uniformly continuous but the same function x2 viewed [0,1]→R is uniformly ...

22 мая 2014 г. · Theorem 2.9: If f is uniformly continuous on a bounded interval I, then f is also bounded to I. I is of the form; [a,b], (a,b], [a,b) or (a,b).

10 мар. 2018 г. · if f and g are uniformly continuous functions, g is bounded and not periodic, f is not necessarily bounded. Then fg is uniformly continuous.

10 окт. 2022 г. · One can show that f is uniformly continuous. Its derivative f′(x)=−2x(1+x2)2.

8 июн. 2011 г. · To do this, we can use the triangle inequality: in general, |a|+|b|≥|a+b|. Set a:=2x0h and b:=h2, and you'll have |2x0h+h2|≤|2x0h|+|h2|.