What is the limit as x approaches 0 of x/(cot(5x)) ?

The limit as x approaches 0 of x/(cot(5x)) is 0

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limit as x approaches 0 of x/(cot(5x))

x \to 0 lim (\frac{x}{cot ( 5 x )})

0

Solution steps

x \to 0 lim (\frac{x}{cot ( 5 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 ( 5 x ) )}

x \to 0 lim (x) = 0

x \to 0 lim (cot (5 x)) = \infty

= \frac{0}{\infty}

Apply Infinity Property:

\frac{0}{\infty} = 0

= 0

\int \frac{1}{1 + v ^{2}} d v

x \to 2 lim (- 4)

\int x e^{- x (1 + y)} d x

e^{2 t} t sin (5 t)

n = 0 \sum \infty (- 1)^{n} x^{2 n}

What is the limit as x approaches 0 of x/(cot(5x)) ?
The limit as x approaches 0 of x/(cot(5x)) is 0