Question Number 104812 by bobhans last updated on 24/Jul/20
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\frac{\mathrm{3}}{{x}}\right)}{\left(\frac{\mathrm{2}}{{x}}+\mathrm{5}\right)^{\mathrm{2}} −\mathrm{25}}\:? \\ $$
Answered by bemath last updated on 24/Jul/20
$${set}\:\frac{\mathrm{1}}{{x}}\:=\:{a}\:,\:{a}\rightarrow\mathrm{0} \\ $$$$\underset{{a}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{3}{a}}{\left(\mathrm{2}{a}+\mathrm{5}\right)^{\mathrm{2}} −\mathrm{25}}\:=\:\underset{{a}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}}{\mathrm{2}.\mathrm{2}\left(\mathrm{2}{a}+\mathrm{5}\right)} \\ $$$$=\:\frac{\mathrm{3}}{\mathrm{20}}\:\bigstar \\ $$