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

\int 6 x^{5} d x

\frac{d}{d x} (\frac{7 x ^{2}}{4 e ^{x} - x})

\frac{\partial}{\partial y} (e^{x y z^{3}} y z^{3})

\int \frac{6}{x ^{2} x ^{2} - 9} d x

d er i v a t i v e \frac{t ^{2} + 1}{t ^{2} - 1}

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