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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\text{logx}-\text{loga}}{\text{x}-\text{a}}$
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Answer

$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\text{logx}-\text{loga}}{\text{x}-\text{a}}$ $=\lim\limits_{\text{x}\rightarrow\text{a}}\frac{\text{log}\frac{\text{x}}{\text{a}}}{\text{a}\Big(\frac{\text{x}}{\text{a}}-1\Big)}$ Let $\text{ h}=\frac{\text{x}}{\text{a}}-1$ $=\frac{1}{\text{a}}\lim\limits_{\text{x}\rightarrow\text{a}}\frac{\text{log(h+1)}}{\text{h}}$ $=\frac{1}{\text{a}}$

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