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Question
\[\lim_{x \to 1/4} \frac{4x - 1}{2\sqrt{x} - 1}\]
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Solution
\[\lim_{x \to 1/4} \left[ \frac{4x - 1}{2\sqrt{x} - 1} \right]\]
\[\text{ It is of the form } \frac{0}{0} . \]
\[ \lim_{x \to 1/4} \left[ \frac{\left( 2\sqrt{x} \right)^2 - 1^2}{2\sqrt{x} - 1} \right]\]
\[ = \lim_{x \to 1/4} \left[ \frac{\left( 2\sqrt{x} - 1 \right)\left( 2\sqrt{x} + 1 \right)}{\left( 2\sqrt{x} - 1 \right)} \right]\]
\[ = 2\sqrt{\frac{1}{4}} + 1\]
\[ = 2 \times \frac{1}{2} + 1\]
\[ = 2\]
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