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

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

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

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

0

Solution steps

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to 0} ( x )}{lim _{x \to 0} ( cot ( x ) )}

x \to 0 lim (x) = 0

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

= \frac{0}{\infty}

Apply Infinity Property:

\frac{0}{\infty} = 0

= 0

x \to 0 lim (x ∣ x ∣)

x \to 1 lim (3 x^{2} + 3)

x \to \infty lim (- 10)

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

x \to 1 + lim (0)

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