Question

$\underset{x\to 1/4}{\lim }\frac{4x-1}{2\sqrt{x}-1}$

Answer 1

$$\begin{gathered} \underset{x\to 1/4}{\lim }\left[\frac{4x-1}{2\sqrt{x}-1}\right] \\ \mathrm{It}\mathrm{is}\mathrm{of}\mathrm{the}\mathrm{form}\frac{0}{0}. \\ \underset{x\to 1/4}{\lim }\left[\frac{{\left(2\sqrt{x}\right)}^2-1^2}{2\sqrt{x}-1}\right] \\ =\underset{x\to 1/4}{\lim }\left[\frac{\left(2\sqrt{x}-1\right)\left(2\sqrt{x}+1\right)}{\left(2\sqrt{x}-1\right)}\right] \\ =2\sqrt{\frac{1}{4}}+1 \\ =2\times \frac{1}{2}+1 \\ =2 \end{gathered}$$