Question: This is real analysis. Exercise 3.4.7: Let f: (0, 1) - R be a bounded continuous function. Show that the function g(x) := x(1 -x)f(x)

This is real analysis.

Exercise 3.4.7: Let f: (0, 1) - R be a bounded continuous function. Show that the function g(x) := x(1 -x)f(x) is uniformly continuous. Exercise 3.4.8: Show that f: (0, co) - R defined by f(x) := sin(1/x) is not uniformly continuous

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