What is the limit as x approaches 0 of (6x)/(cot(x)) ?

The limit as x approaches 0 of (6x)/(cot(x)) is 0

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limit as x approaches 0 of (6x)/(cot(x))

x \to 0 lim (\frac{6 x}{cot ( x )})

0

Solution steps

x \to 0 lim (\frac{6 x}{cot ( x )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 6 \cdot 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

= 6 \cdot \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

= 6 \cdot \frac{0}{\infty}

Simplify

6 \cdot \frac{0}{\infty} : 0

= 0

x \to - 1 lim (3 x (2 x - 1))

x \to 3 lim ((x - 3) (x - 4))

x \to 3 lim (2 x^{2} - 7)

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

x \to 0 - lim (6 (\frac{1}{x} - cot (x)))

What is the limit as x approaches 0 of (6x)/(cot(x)) ?
The limit as x approaches 0 of (6x)/(cot(x)) is 0