limit as x approaches 2pi-of xcsc(x)

解

x \to 2 π - lim (x csc (x))

- \infty

解答ステップ

x \to 2 π - lim (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 2 π - lim (x) \cdot x \to 2 π - lim (csc (x))

x \to 2 π - lim (x) = 2 π

x \to 2 π - lim (csc (x)) = - \infty

= 2 π (- \infty)

無限大の特性を適用する:

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

= - \infty