Question Number 208381 by hardmath last updated on 14/Jun/24
$$\mathrm{g}\left(\mathrm{x}\right)\:=\:\mathrm{lnx}^{\mathrm{2}} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:+\:\mathrm{25}} \\ $$$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\boldsymbol{\mathrm{e}}} {\mathrm{lim}}\:\left(\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)\:=\:?\right. \\ $$
Answered by A5T last updated on 14/Jun/24
$${f}\left({g}\left({x}\right)\right)=\sqrt[{\mathrm{3}}]{{ln}\left({x}^{\mathrm{2}} \right)+\mathrm{25}} \\ $$$$\Rightarrow\underset{{x}\rightarrow{e}} {{lim}f}\left({g}\left({x}\right)\right)=\sqrt[{\mathrm{3}}]{{ln}\left({e}^{\mathrm{2}} \right)+\mathrm{25}}=\sqrt[{\mathrm{3}}]{\mathrm{27}}=\mathrm{3} \\ $$