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Limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{3\sin\text{x}-4\sin^3\text{x}}{\text{x}}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{3\sin\text{x}-4\sin^3\text{x}}{\text{x}}$
$=\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{{\text{x}}}$ $\big[\because\sin3\text{x}=3\sin\text{x}-4\sin^3\text{x}\big]$
$=\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{{3\text{x}}}\times3$
$=3\times\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{{3\text{x}}}$
$=3\times\lim\limits_{3\text{x}\rightarrow0}\frac{\sin3\text{x}}{{3\text{x}}}$ $\big[\because\text{x}\rightarrow0,3\text{x}\rightarrow0\big]$
$=3\times1$ $\Big[\because\ \lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}}{\text{x}}=1\Big]$
$=3$

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