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Question
\[\lim_{x \to 0} \frac{\tan^2 3x}{x^2}\]
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Solution
\[\lim_{x \to 0} \left[ \frac{\tan^2 3x}{x^2} \right]\]
\[= \lim_{x \to 0} \left[ \frac{\tan 3x}{3x} \times \frac{\tan 3x}{3x} \right] \times 9\]
\[ = 1 \times 1 \times 9 \left[ \because \lim_{x \to 0} \frac{\tan x}{x} = 1 \right]\]
\[ = 9\]
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