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Limits — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\tan^23\text{x}}{\text{x}^2}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\tan^23\text{x}}{\text{x}^2}$
$=\Big(\lim\limits_{\text{x}\rightarrow0}\frac{\tan3\text{x}}{\text{x}}\Big)^2$
$=\Big(\lim\limits_{\text{x}\rightarrow0}\frac{\tan3\text{x}}{3\text{x}}\Big)^2$
$=1\times9$ $\Big[\because\ \lim\limits_{\text{x}\rightarrow0}\frac{\tan\text{x}}{\text{x}}=1\Big]$
$=9$

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