Choose and work either a) or b), NOT BOTH. (a) Show that the function f (x) = sin x for x ER is uniformly continuous. (b) Show that the function k(x) = sin(1/x) is not uniformly continuous on the set D(k) = {r € F : 0
Choose and work either a) or b), NOT BOTH. (a) Show that the function f (x) = sin x for x ER is uniformly continuous. (b) Show that the function k(x) = sin(1/x) is not uniformly continuous on the set D(k) = {r € F : 0
Choose and work either a) or b), NOT BOTH. (a) Show that the function f (x) = sin x for x ER is uniformly continuous. (b) Show that the function k(x) = sin(1/x) is not uniformly continuous on the set D(k) = {r € F : 0
Transcribed Image Text:4. Choose and work either a) or b), NOT BOTH.
(a) Show that the function f(x) = sin x for x ER is uniformly continuous.
(b) Show that the function k(x) = sin(1/x) is not uniformly continuous on the set
D(k) = {x € F : 0 < x}.
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Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.
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