Let [itex]\{h_n\}[/itex] be ANY sequence of real numbers such that [itex]h_n \neq 0[/tex] and [itex]h_n \to 0[/itex]. If [itex]f'(x)[/itex] exists, do we have(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

f'(x) = \lim_{n\to \infty} f_n(x),

[/tex]

where

[tex]

f_n(x) = \frac{1}{h_n} (f(x+h_n) - f(x))

[/tex]

????

This seems to express the derivative as the pointwise limit of a sequence of functions...right? Do we know, in addition, that the convergence is uniform?

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# Question about defn. of derivative

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