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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits1 Mark
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow\frac{1}{4}}\frac{4\text{x}-1}{2\sqrt{\text{x}}-1}$
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Answer

$\lim\limits_{\text{x}\rightarrow\frac{1}{4}}\frac{4\text{x}-1}{2\sqrt{\text{x}}-1}$ $=\lim\limits_{\text{x}\rightarrow\frac{1}{4}}\frac{4\Big(\text{x}-\frac14\Big)}{2\Big(\sqrt{\text{x}}-\frac12\Big)}$ $=\lim\limits_{\text{x}\rightarrow\frac{1}{4}}\frac{\Big(\sqrt{\text{x}}-\frac12\Big)\Big(\sqrt{\text{x}}+\frac12\Big)}{2\Big(\sqrt{\text{x}}-\frac12\Big)}$ $=\lim\limits_{\text{x}\rightarrow\frac14}\frac{\Big(\sqrt{\text{x}}+\frac12\Big)}{2}$ $=\frac{4\big(\frac12+\frac12\big)}{2}$ $=\frac{4(1)}{2}=2$

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