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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limits: $\lim\limits_{\text{x}\rightarrow\infty}\frac{\text{x}}{\sqrt{4\text{x}^2+1}-1}$
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Answer

$\lim\limits_{\text{x}\rightarrow\infty}\frac{\text{x}}{\sqrt{4\text{x}^2+1}-1}$ $=\lim\limits_{\text{x}\rightarrow\infty}\frac{1}{\sqrt{4+\frac{1}{\text{x}^2}}-\frac{1}{\text{x}}}$ $=\frac{1}{\sqrt{4}-0}$ $=\frac12$

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