4. We say that a function f(z) is bounded if there exists real numbers m and M such that for all real numbers 1, m≤ f(x) ≤ M. (Examples include sin(x) and cos(x), letting m = -1 and M = 1.) (a) Let f(z) be any bounded function and g(z) be a function such that lim g(x) = 0. Explain why the following argument is incorrect: z-+b lim f(x)g(x) = H [lim f(x)] [lim g(x)] [lim f(x)].0 0

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