What is the limit as x approaches pi-of xcot(x) ?

The limit as x approaches pi-of xcot(x) is -infinity

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limit as x approaches pi-of xcot(x)

x \to π - lim (x cot (x))

- \infty

Solution steps

x \to π - lim (x cot (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 (x) \cdot x \to π - lim (cot (x))

x \to π - lim (x) = π

x \to π - lim (cot (x)) = - \infty

= π (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 1 lim (1 + 3 x - 1)

x \to \infty lim (\frac{1}{+ x})

x \to 3 - lim (\frac{4 x - 12}{x - 3})

x \to - \frac{1}{2} lim (- \frac{7}{∣ 2 x + 1 ∣})

x \to 0 lim ([x - 2] \cdot [x + 3])

What is the limit as x approaches pi-of xcot(x) ?
The limit as x approaches pi-of xcot(x) is -infinity