limit as x approaches 0 of (9sin(x))/(\sqrt[3]{x)}

解

x \to 0 lim (\frac{9 sin ( x )}{3 x})

0

解答ステップ

x \to 0 lim (\frac{9 sin ( x )}{3 x})

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

= 9 \cdot x \to 0 lim (\frac{sin ( x )}{3 x})

ロピタルの定理を適用する

= 9 \cdot x \to 0 lim (\frac{cos ( x )}{\frac{1}{3 x ^{\frac{2}{3}}}})

簡素化

= 9 \cdot x \to 0 lim (3 x^{\frac{2}{3}} cos (x))

値を挿入する

x = 0

= 9 \cdot 3 \cdot 0^{\frac{2}{3}} cos (0)

簡素化

9 \cdot 3 \cdot 0^{\frac{2}{3}} cos (0) : 0

= 0