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

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

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limit as x approaches pi+of-cot(x)csc(x)

x \to π + lim (- cot (x) csc (x))

\infty

Solution steps

x \to π + lim (- cot (x) csc (x))

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

= - x \to π + 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 π + lim (cot (x)) \cdot x \to π + lim (csc (x))

x \to π + lim (cot (x)) = \infty

x \to π + lim (csc (x)) = - \infty

= - \infty \cdot (- \infty)

Apply Infinity Property:

- \infty (- \infty) = \infty

= \infty

x \to \infty lim (\frac{5}{7})

n \to \infty lim (n + 2)

x \to 0 lim (sin (\frac{1}{x}) + 1)

x \to - \infty lim (x^{2} - 3 x)

x \to 1 lim (cos (\frac{π x}{2}))

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