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Where-f-x-4x-2-1-2x-1-defined-in-R-1-2-determine-lim-x-1-2-f-x-




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

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