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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{log(2+x)}+\text{log0.5}}{\text{x}}$
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Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{log(2+x)}+\text{log0.5}}{\text{x}}$ $=\lim\limits_{\text{x}\rightarrow0}\frac{\text{log}\Big(1+\frac{\text{x}}{2}\Big)}{2\Big(\frac{\text{x}}{2}\Big)}$ $=\frac{1}{2}$

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