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Limits — MATHS STD 11 Science — Question

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

$\lim\limits_{\text{x}\rightarrow0}\frac{\log\text{(a}+\text{x})-\log\text{a}}{\text{x}}$ $=\lim\limits_{\text{x}\rightarrow0}\frac{\log\text{}\big(1+\frac{\text{x}}{\text{a}}\big)}{\text{a}\big(\frac{\text{x}}{\text{a}}\big)}$ $=\frac{1}{\text{a}}$

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