limit as x approaches 0 of (arcsin(x))/(7x)

解

x \to 0 lim (\frac{arcsin ( x )}{7 x})

\frac{1}{7}

十進法表記

0.14285 \dots

解答ステップ

x \to 0 lim (\frac{arcsin ( x )}{7 x})

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

= \frac{1}{7} \cdot x \to 0 lim (\frac{arcsin ( x )}{x})

ロピタルの定理を適用する

= \frac{1}{7} \cdot x \to 0 lim (\frac{\frac{1}{1 - x ^{2}}}{1})

値を挿入する

x = 0

= \frac{1}{7} \cdot \frac{\frac{1}{1 - 0 ^{2}}}{1}

簡素化

\frac{1}{7} \cdot \frac{\frac{1}{1 - 0 ^{2}}}{1} : \frac{1}{7}

= \frac{1}{7}