Assumptions Matter Suppose f (x) = x (2 + sin x) and let g(x) = x2 + 1. (a) Show directly that lim f(x)/g(x) = 0. (b) Show that lim f(x) = lim g (x) = 0, but lim f'(x)/g'(x) does not exist. Do (a) and (b) contradict L'Hôpital's Rule? Explain.

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