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evaluate lim x tends to 0 tan?3x / x?

\lim_{x \to 0} \frac{\tan^{2} 3 x}{x^{2}} = \lim_{x \to 0} \frac{{(\tan 3 x)}^{2}}{x^{2}} = \lim_{x \to 0} \frac{3^{2} {(\tan 3 x)}^{2}}{3^{2} x^{2}} = \lim_{x \to 0} 9 {(\frac{\tan 3 x}{3 x})}^{2} L e t 3 x = y, n o t e a s x t e n d t o z e r o y t e n d s t o z e r o \lim_{x \to 0} 9 {(\frac{\tan 3 x}{3 x})}^{2} = \lim_{y \to 0} 9 {(\frac{\tan y}{y})}^{2} = 9 {(\lim_{y \to 0} \frac{\tan y}{y})}^{2} \sin c e \lim_{y \to 0} \frac{\tan y}{y} = 1 \lim_{x \to 0} 9 {(\frac{\tan 3 x}{3 x})}^{2} = \lim_{y \to 0} 9 {(\frac{\tan y}{y})}^{2} = 9 {(\lim_{y \to 0} \frac{\tan y}{y})}^{2} = 9

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