L-Hopital-rule-lim-x-f-x-g-x-lim-x-f-x-g-x-f-g-f-x-d-dx-f-x-g-x-d-dx-g-x-differential-What-is-it-Proof-of-the-rule-plz-

Question Number 54506 by kwonjun1202 last updated on 05/Feb/19

L′Hopital rule lim_(x→α) ((f(x))/(g(x)))=lim_(x→α) ((f ′(x))/(g′(x)))= ((f ′(α))/(g′(α))) f ′(x)=(d/dx)f(x) , g′(x)=(d/dx)g(x) differential What is it? Proof of the rule.. plz :)

$${L}'{Hopital}\:{rule} \\ $$$$\underset{{x}\rightarrow\alpha} {\mathrm{lim}}\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}=\underset{{x}\rightarrow\alpha} {\mathrm{lim}}\:\frac{{f}\:'\left({x}\right)}{{g}'\left({x}\right)}=\:\frac{{f}\:'\left(\alpha\right)}{{g}'\left(\alpha\right)} \\ $$$${f}\:'\left({x}\right)=\frac{{d}}{{dx}}{f}\left({x}\right)\:,\:{g}'\left({x}\right)=\frac{{d}}{{dx}}{g}\left({x}\right)\:{differential} \\ $$$$\left.{What}\:{is}\:{it}?\:{Proof}\:{of}\:{the}\:{rule}..\:\mathrm{plz}\::\right) \\ $$

Answered by kaivan.ahmadi last updated on 05/Feb/19