Question Number 76667 by naka3546 last updated on 29/Dec/19
Commented by benjo 1/2 santuyy last updated on 29/Dec/19
$${using}\:{L}'{Hopital}\:{Rule}\: \\ $$
Answered by john santu last updated on 29/Dec/19
$$\underset{{x}\rightarrow\propto} {\mathrm{lim}}\:\frac{{f}\left({f}^{−\mathrm{1}} \left(\mathrm{8}{x}\right)\right)−{f}\left({f}^{−\mathrm{1}} \left({x}\right)\right)}{{f}\left({x}^{\frac{\mathrm{1}}{\mathrm{3}}} \right)}\:= \\ $$$$\underset{{x}\rightarrow\propto} {\mathrm{lim}}\:\frac{\mathrm{8}{x}−{x}}{\mathrm{8}{x}+\mathrm{3}{x}^{\frac{\mathrm{1}}{\mathrm{3}}} }\:=\:\underset{{x}\rightarrow\propto} {\mathrm{lim}}\:\frac{\mathrm{7}{x}}{\mathrm{8}{x}+\mathrm{3}{x}^{\frac{\mathrm{1}}{\mathrm{3}}} }\:=\:\frac{\mathrm{7}}{\mathrm{8}}\:\blacksquare \\ $$
Commented by mr W last updated on 30/Dec/19
$${how}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{f}^{−\mathrm{1}} \left({g}\left({x}\right)\right)}{{h}\left({x}\right)}=\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{g}\left({x}\right)}{{f}\left({h}\left({x}\right)\right)}\:? \\ $$
Commented by benjo 1/2 santuyy last updated on 30/Dec/19
$${sir}\:{W}\:{what}\:{this}\:{Answer}\:{correct}? \\ $$
Commented by mr W last updated on 30/Dec/19
$${probably}\:{not}. \\ $$
Answered by benjo 1/2 santuyy last updated on 30/Dec/19
$${i}\:{solved}\:{it}\:{with}\:{the}\:{Hopital}\:{theorem} \\ $$
Commented by mr W last updated on 31/Dec/19
$${your}\:{result}? \\ $$