limit as x approaches pi/4 of (tan(4x))/(4x-pi)

解答

x \to \frac{π}{4} lim (\frac{tan ( 4 x )}{4 x - π})

1

求解步骤

x \to \frac{π}{4} lim (\frac{tan ( 4 x )}{4 x - π})

使用洛必达法则

= x \to \frac{π}{4} lim (\frac{sec ^{2} ( 4 x ) \cdot 4}{4})

代入值

x = \frac{π}{4}

= \frac{sec ^{2} ( 4 \cdot \frac{π}{4} ) \cdot 4}{4}

化简

\frac{sec ^{2} ( 4 \cdot \frac{π}{4} ) \cdot 4}{4} : 1

= 1

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