A function f is defined to be bounded if there is some number B > 0...

  

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A function f is defined to be bounded if there is some number B > 0 such that -B < f(x) < B for all values of x. Suppose that f is bounded and that g is continuous at 0 and that g(0) = 0. Prove that the product function fg is also continuous at 0. A function f is defined to be bounded if there is some number B > 0 such that -B < f(x) < B for all values of x. Suppose that f is bounded and that g is continuous at 0 and that g(0) = 0. Prove that the product function fg is also continuous at 0.