f-function-continue-at-o-and-lim-x-0-f-2x-f-x-x-l-prove-that-f-is-derivable-at-o-and-f-0-l-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 30509 by abdo imad last updated on 22/Feb/18

f function continue at o and lim_(x→0) ((f(2x)−f(x))/x)=l prove that f is derivable at o and f^′ (0)=l.

$${f}\:{function}\:{continue}\:{at}\:{o}\:{and}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{f}\left(\mathrm{2}{x}\right)−{f}\left({x}\right)}{{x}}={l} \\ $$$${prove}\:{that}\:{f}\:{is}\:{derivable}\:{at}\:{o}\:{and}\:{f}^{'} \left(\mathrm{0}\right)={l}. \\ $$

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f-function-continue-at-o-and-lim-x-0-f-2x-f-x-x-l-prove-that-f-is-derivable-at-o-and-f-0-l-

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