limit as h approaches 0 of (sin(h))/(6h)

解

h \to 0 lim (\frac{sin ( h )}{6 h})

\frac{1}{6}

十進法表記

0.16666 \dots

解答ステップ

h \to 0 lim (\frac{sin ( h )}{6 h})

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

= \frac{1}{6} \cdot h \to 0 lim (\frac{sin ( h )}{h})

ロピタルの定理を適用する

= \frac{1}{6} \cdot h \to 0 lim (\frac{cos ( h )}{1})

値を挿入する

h = 0

= \frac{1}{6} \cdot \frac{cos ( 0 )}{1}

簡素化

\frac{1}{6} \cdot \frac{cos ( 0 )}{1} : \frac{1}{6}

= \frac{1}{6}