Question Number 156024 by alcohol last updated on 07/Oct/21
Answered by mr W last updated on 07/Oct/21
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{1}+{f}\left(\mathrm{3}{x}\right)}}{{x}} \\ $$$$=\mathrm{3}\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{1}+{f}\left(\mathrm{3}{x}\right)}}{\mathrm{3}{x}} \\ $$$$=\mathrm{3}\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{1}+{f}\left({t}\right)}}{{t}} \\ $$$$=\mathrm{3}{l} \\ $$