Unformatted text preview: ). ii) Prove that f is uniformly continuous on [1 , 2] by assuming the fact that f is continuous on (0 , + ∞ ). iii) Prove that f is uniformly continuous on [1 , + ∞ ) by using the ǫ − δ property in De±nition 19.1. 3. i) Let f, g be uniformly continuous functions on ( a, b ). Show that the function f + g is uniformly continuous on ( a, b ) by using the ǫ − δ property in De±nition 19.1. ii) Let f be a function on ( a, b ). Suppose that f is uniformly continuous on ( a, c ] and [ c, b ) for some c such that a < c < b . Then, Prove that f is uniformly continuous on ( a, b ) by using the ǫ − δ property in De±nition 19.1. 1...
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 Fall '07
 Fukuda
 Continuous function, Uniform continuity, uniformly continuous functions, MAT 125A Homework

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