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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits1 Mark
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{4}}\frac{\text{x}^2-16}{\sqrt{\text{x}}-2}$
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Answer

$\lim\limits_{\text{x}\rightarrow{4}}\frac{\text{x}^2-16}{\sqrt{\text{x}}-2}$ $=\lim\limits_{\text{x}\rightarrow{4}}\frac{(\text{x}-4)(\text{x}+4)}{\big(\sqrt{\text{x}}-2\big)}$ $=\lim\limits_{\text{x}\rightarrow{4}}\frac{\big(\sqrt{\text{x}}-2\big)\big(\sqrt{\text{x}}+2\big)(\text{x}+4)}{\big(\sqrt{\text{x}}-2\big)}$ $=\lim\limits_{\text{x}\rightarrow4}{\Big(\sqrt{\text{x}}+2\Big)}{(\text{x}+4)}$ $=(2+2)(4+4)$ $=4(8)$ $=32$

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