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2.6 Emerging Doubts (continued)Cauchy's CounterexampleThe death knell for Lagrange's
definition of the derivative was sounded by Cauchy
in 1821. He exhibited a counterexample to Lagrange's assertion that distinct
functions have distinct power series: All of the derivatives of f(x) at x=0 are equal to 0. At x=0, this function has the same power series expansion as the constant function 0. The determination of the derivatives of f(x) at x=0 will be demonstrated in section 3.3. 
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