(Requires calculus)
a) Show that if f(x) and g(x) are functions such that f(x) is o(g(x)) and c is a constant, then cf(x) is o(g(x)). where (cf)(x) = cf(x).
b) Show that if f1(x), is f2(x), and g(x) are functions such that f1(x) is o(g(x)) and f2(x) is o(g(x)), then (f1 + f2)(x) is o(g(x)), where (f1 + f2)(x) = f1(x) + f2(x).
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