limit as x approaches 0 of-cot(x)csc(x)

解

x \to 0 lim (- cot (x) csc (x))

- \infty

解答ステップ

x \to 0 lim (- cot (x) csc (x))

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

= - x \to 0 lim (cot (x) csc (x))

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

不定形式の場合を除く

= - x \to 0 lim (cot (x)) \cdot x \to 0 lim (csc (x))

x \to 0 lim (cot (x)) = \infty

x \to 0 lim (csc (x)) = \infty

= - \infty \cdot \infty

無限大の特性を適用する:

- \infty \infty = - \infty

= - \infty