Given a convergent sequence [tex]x_n \rightarrow x[/tex] and a function f, is(adsbygoogle = window.adsbygoogle || []).push({});

[tex] lim_{n \rightarrow \infty} \frac{f(x_n) - f(x_{n-1})}{x_n - x_{n-1}} = f'(x) [/tex] ?

I believe it it is, but I haven't been able to figure out how to prove it. Does anyone know of a proof or counter-example?

And probably should add [tex] x_n \not = x_{n-1} \forall n [/tex]

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# Is function of convergent sequence rate of change equal to derivative?

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