Uniformly Continuous - Let E be a nonempty subset of R and f:E-->R. State the definition f is uniformly continuous on E. Prove f(x) =x^2 is uniformly continuous on the interval[0,1].
keywords: uniform continuity
Proving that f is not uniformly continuous - The following theorem could be used to write the proof.
A theorem states that if d:D-->R is uniformly continuous on D iff the following
condition is satisfied:
If un and vn are both sequences in D ...
Uniformly Continuous Functions and Mean Value Theorem - Assume that f is differentiable for each x and there exists M>0
such that
for each x
Prove that f is uniformly continuous on D.
Hint: Can use the mean value theo ...
Real Analysis - Continuous Functions - State precisely and prove: A uniformly continuous function of a uniformly continuous function is uniformly continuous.