Question Number 71000 by Maclaurin Stickker last updated on 10/Oct/19
$${Where}\:{f}\left({x}\right)=\frac{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}{x}−\mathrm{1}}\:{defined}\:{in}\: \\ $$$$\mathbb{R}−\left\{\frac{\mathrm{1}}{\mathrm{2}}\right\},\:{determine}\:\underset{{x}\rightarrow\frac{\mathrm{1}}{\mathrm{2}}} {\mathrm{lim}}{f}\left({x}\right). \\ $$
Commented by mathmax by abdo last updated on 10/Oct/19
$${lim}_{{x}\rightarrow\frac{\mathrm{1}}{\mathrm{2}}} \:{f}\left({x}\right)={lim}_{{x}\rightarrow\frac{\mathrm{1}}{\mathrm{2}}} \:\:\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{1}\right)}{\mathrm{2}{x}−\mathrm{1}}\:={lim}_{{x}\rightarrow\frac{\mathrm{1}}{\mathrm{2}}} \left(\mathrm{2}{x}+\mathrm{1}\right)=\mathrm{2} \\ $$