limit as x approaches pi/4 of 7tan^{tan(2x)}(x)

解答

x \to \frac{π}{4} lim (7 tan^{t a n (2 x)} (x))

\frac{7}{e}

十进制

2.57515 \dots

求解步骤

x \to \frac{π}{4} lim (7 tan^{t a n (2 x)} (x))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 7 \cdot x \to \frac{π}{4} lim (tan^{t a n (2 x)} (x))

使用指数运算法则

= 7 \cdot x \to \frac{π}{4} lim (e^{t a n (2 x) l n (t a n (x))})

使用极限链式法则:

\frac{1}{e}

= 7 \cdot \frac{1}{e}

化简

7 \cdot \frac{1}{e} : \frac{7}{e}

= \frac{7}{e}

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