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

The limit as x approaches 0 of (1-cot(x))/(1/x) is -1

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limit as x approaches 0 of (1-cot(x))/(1/x)

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

- 1

Solution steps

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

Expand

\frac{1 - cot ( x )}{\frac{1}{x}} : x - x cot (x)

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

x \to 0 lim (x) = 0

x \to 0 lim (x cot (x)) = 1

= 0 - 1

Simplify

= - 1

5 + x^{2}

\frac{\partial}{\partial x} (2 y - x^{2})

\frac{d}{d x} (\frac{( x ^{2} - 5 x )}{x + 1})

\int \frac{x + 5}{5 - x} d x

\frac{d}{d x} ((5 x^{3} - 8)^{10})

What is the limit as x approaches 0 of (1-cot(x))/(1/x) ?
The limit as x approaches 0 of (1-cot(x))/(1/x) is -1