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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives3 Marks
Question
Evaluate:
$\lim\limits_{\text{x} \rightarrow 0}\frac{\sin3\text{x}}{\sin7\text{x}}$
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Answer

Given that $\lim\limits_{\text{x} \rightarrow 0}\frac{\sin3\text{x}}{\sin7\text{x}}$
$=\lim\limits_{\text{x} \rightarrow 0}\frac{\frac{\sin3\text{x}}{3\text{x}}\times3\text{x}}{\frac{\sin7\text{x}}{7\text{x}}\times7\text{x}}$
$=\frac{\lim\limits_{3\text{x} \rightarrow 0}\Big(\frac{\sin3\text{x}}{3\text{x}}\Big)}{\lim\limits_{7\text{x} \rightarrow 0}\Big(\frac{\sin7\text{x}}{7\text{x}}\Big)}\times\frac{3}{7}$
$=\frac{1}{1}\times\frac{3}{7}=\frac{3}{7}$
Hence, the required answer is $\frac{3}{7}.$

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