limit as x approaches 0-of csc(x)(x-1)

解

x \to 0 - lim (csc (x) (x - 1))

\infty

解答ステップ

x \to 0 - lim (csc (x) (x - 1))

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 (csc (x)) \cdot x \to 0 - lim (x - 1)

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

x \to 0 - lim (x - 1) = - 1

= (- \infty) (- 1)

無限大の特性を適用する:

- c \cdot (- \infty) = \infty

= \infty