limit as x approaches infinity of (arctan(4x))/8

解答

x \to \infty lim (\frac{arctan ( 4 x )}{8})

\frac{π}{16}

十进制

0.19634 \dots

求解步骤

x \to \infty lim (\frac{arctan ( 4 x )}{8})

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

= \frac{1}{8} \cdot x \to \infty lim (arctan (4 x))

使用极限链式法则:

\frac{π}{2}

= \frac{1}{8} \cdot \frac{π}{2}

化简

\frac{1}{8} \cdot \frac{π}{2} : \frac{π}{16}

= \frac{π}{16}

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