limit as x approaches 0 of 7cot^4(3x)

解

x \to 0 lim (7 cot^{4} (3 x))

\infty

解答ステップ

x \to 0 lim (7 cot^{4} (3 x))

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

= 7 \cdot x \to 0 lim (cot^{4} (3 x))

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

不定形式の場合を除く

= 7 (x \to 0 lim (cot (3 x)))^{4}

連鎖法則の制限を適用する:

\infty

= 7 \infty^{4}

簡素化

7 \infty^{4} : \infty

= \infty