Question: Let f(x), g)u), v(x) be four positive functions from R to R such that f(x) 0(g(x)) and u(z) = 0(v(x). For each claim below, prove

Let f(x), g)u), v(x) be four positive functions from R to R such that f(x) 0(g(x)) and u(z) = 0(v(x). For each claim below, prove it or give a counterexample. (a) f(x) + u(z) = 0(g(x) + u(z)) (b) f(x) . u(z) = 0(g(x) , u(z)) (c) f(x)u)O(g()) (d) f(a(z)) = 0(g(v(x)))

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