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False statement give a counter example. Can someone explain to me why this statement is false:

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"If limx→a f(x)/g(x) exists and is finite for two functions f and g that are continuous at a, then g(a)≠0" and could you give a counterexample. thanks in advance

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Let f(x) = g(x) = x. Let a = 0. Functions f and g are continuous over all real numbers. f(x)/g(x) = 1 for all x ≠ a lim f(x)/g(x) = 1 x→a g(a) = 0

            
        

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