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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{3^{2+\text{x}}-9}{\text{x}}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{3^{2+\text{x}}-9}{\text{x}}=\lim\limits_{\text{x}\rightarrow0}\frac{3^2.3^\text{x}-9}{\text{x}}$
$=9\lim\limits_{\text{x}\rightarrow0}\frac{3^\text{x}-1}{\text{x}}$
$=9 \text{log}_\text{e}3$

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