Menu Close

Question-76667




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

Leave a Reply

Your email address will not be published. Required fields are marked *