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    Limit of quotient of two functions

    Let f(x) and g(x) be functions. Then if limit of f(x)/g(x) = 1. That implies lim f(x) = lim g(x) right? Consider this proof. lim f(x)/g(x) = 1 lim f(x) x lim 1/g(x) = 1 lim f(x) = 1 / (lim 1/g(x)) lim f(x) = lim g(x).
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