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

解答

x \to 2 π - lim ((x) csc (x))

- \infty

求解步骤

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)

不定型除外

= 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)

运用无穷大属性:

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

= - \infty

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