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

解答

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

\infty

求解步骤

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)

不定型除外

= 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)

运用无穷大属性:

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

= \infty

\int_{- \infty}^{0} x^{2} e^{x} d x

\int 1 + \frac{1}{2 x} d x

\int_{1}^{3} e^{x} d x

\int_{3}^{6} \frac{x}{x ^{2} + 6 x + 13} d x

\frac{\partial}{\partial y} (2 x^{4 y})