- Question One 5 Marks Let F Be A Real Uniformly Continuous Function On A A Bounded Set Ein R Prove That Is Bounded On 1 (187.25 KiB) Viewed 31 times
please solve all
Question One: (5 Marks) Let f be a real uniformly continuous function on a a bounded set Ein R. Prove that is bounded on E Question Two: (5 Marks) Let f be a real uniformly continuous function on a bounded set Ein R. Prove that f is bounded on E. Question Three: (5 Marks) Let f = sin(!), 0 <I<1. Is s uniformly con- timuous function (0,1). Question Four: (5 Marks) Supposef is a bounded real function on (a, b), and BERS (0,(4,01). Does it follows that se RS (0, [a, b]). Does the answer change if we assume that f' € RS (0, 0,6]). 2 22 let felR IR be continuous show that f is uniformly on the IR if lin on the IR if lin f(x) is fimile x → GOOD LUCK