limit as x approaches 0 of (tan(12x))/x

解答

x \to 0 lim (\frac{tan ( 12 x )}{x})

12

求解步骤

x \to 0 lim (\frac{tan ( 12 x )}{x})

使用洛必达法则

= x \to 0 lim (\frac{sec ^{2} ( 12 x ) \cdot 12}{1})

代入值

x = 0

= \frac{sec ^{2} ( 12 \cdot 0 ) \cdot 12}{1}

化简

\frac{sec ^{2} ( 12 \cdot 0 ) \cdot 12}{1} : 12

= 12

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