Question Number 149373 by fotosy2k last updated on 05/Aug/21
Answered by john_santu last updated on 05/Aug/21
$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+\frac{\mathrm{3x}}{\mathrm{2}}\right)−\left(\mathrm{1}+\frac{\mathrm{2x}}{\mathrm{2}}\right)}{\mathrm{x}\left(\mathrm{1}+\mathrm{2x}\right)} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{x}}\:×\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2x}}=\:\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{1}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by fotosy2k last updated on 05/Aug/21
$${thank}\:{you} \\ $$