Evaluate the following limit: _ x 0 3x 5x - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{5\text{x}}$

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Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{5\text{x}}$ $=\frac{1}{5}\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{3\text{x}}\times3$ $=\frac35\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{3\text{x}}$ $=\frac{3}{5}\times1$ $\Big[\because\ \lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}}{\text{x}}=1\Big]$ $=\frac{3}{5}$

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