What is the limit as x approaches 0 of 1/(xcot(3x)) ?

The limit as x approaches 0 of 1/(xcot(3x)) is 3

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limit as x approaches 0 of 1/(xcot(3x))

x \to 0 lim (\frac{1}{x cot ( 3 x )})

3

Solution steps

x \to 0 lim (\frac{1}{x cot ( 3 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} ( 1 )}{lim _{x \to 0} ( x cot ( 3 x ) )}

x \to 0 lim (1) = 1

x \to 0 lim (x cot (3 x)) = \frac{1}{3}

= \frac{1}{\frac{1}{3}}

Simplify

= 3

x \to 0 lim (\frac{8 ^{x} - 2 ^{x}}{x})

x \to \infty lim (\frac{arctan ( 4 x )}{8})

x \to 0 lim (\frac{x}{sec ( 4 x )})

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

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

What is the limit as x approaches 0 of 1/(xcot(3x)) ?
The limit as x approaches 0 of 1/(xcot(3x)) is 3