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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{3^{2+\text{x}}-9}{\text{x}}$
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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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