What is the limit as x approaches 0 of (cot(x))^2 ?

The limit as x approaches 0 of (cot(x))^2 is infinity

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limit as x approaches 0 of (cot(x))^2

x \to 0 lim ((cot (x))^{2})

\infty

Solution steps

x \to 0 lim ((cot (x))^{2})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= (x \to 0 lim (cot (x)))^{2}

Apply the common limit:

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

= \infty^{2}

Apply Infinity Property:

\infty^{c} = \infty

= \infty

x \to 1 lim (1 - x + [x] - [1 - x])

x \to 0 lim (\frac{1}{e ^{\frac{1}{x}} - 1})

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

x \to 4 lim (4 x^{3} - 3 x - 5)

x \to 5 + lim (\frac{x}{x ^{2} - 25})

What is the limit as x approaches 0 of (cot(x))^2 ?
The limit as x approaches 0 of (cot(x))^2 is infinity