What is the limit as x approaches 0-of csc(x)(x-1) ?

The limit as x approaches 0-of csc(x)(x-1) is infinity

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

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

\infty

Solution steps

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)

With the exception of indeterminate form

= 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)

Apply Infinity Property:

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

= \infty

What is the limit as x approaches 0-of csc(x)(x-1) ?
The limit as x approaches 0-of csc(x)(x-1) is infinity