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Question
\[\lim_{x \to 0} \frac{\sin 5x}{\tan 3x}\]
Solution
\[\lim_{x \to 0} \left[ \frac{\sin 5x}{\tan 3x} \right]\]
\[\Rightarrow \lim_{x \to 0} \left[ \lim_{x \to 0} \frac{\sin 5x}{5x} \times \frac{5x}{\frac{\tan 3x}{3x} \times 3x} \right]\]
\[ \Rightarrow \frac{5}{3} \left[ \because \lim_{x \to 0} \frac{\sin x}{x} = 1, \lim_{x \to 0} \frac{\tan x}{x} = 1 \right]\]
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