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

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

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

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

- \infty

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - x \to 0 lim (cot (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)

With the exception of indeterminate form

= - x \to 0 lim (cot (x)) \cdot x \to 0 lim (csc (x))

x \to 0 lim (cot (x)) = \infty

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

= - \infty \cdot \infty

Apply Infinity Property:

- \infty \infty = - \infty

= - \infty

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