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Limits — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{8^\text{x}-2^\text{x}}{\text{x}}$
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Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{8^\text{x}-2^\text{x}}{\text{x}}$
$=\lim\limits_{\text{x}\rightarrow0}\frac{8^\text{x}-1}{\text{x}}-\lim\limits_{\text{x}\rightarrow0}\frac{2^\text{x}-1}{\text{x}}$
$=\text{log8}-\text{log2}$
$=\text{log4}$

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