What is the limit as x approaches 0 of (8x)/(cot(x)) ?

The limit as x approaches 0 of (8x)/(cot(x)) is 0

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limit as x approaches 0 of (8x)/(cot(x))

x \to 0 lim (\frac{8 x}{cot ( x )})

0

Solution steps

x \to 0 lim (\frac{8 x}{cot ( x )})

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

= 8 \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

= 8 \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

= 8 \cdot \frac{0}{\infty}

Simplify

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

= 0

3 x^{2} + x, at x = 1

(- 6, 4), (- 5, - 10)

f (x) = 7 x^{2}, at x = 4

\frac{d}{d x} (\frac{x + 3}{x - 1})

e^{y} \cdot (\frac{d y}{d x} + 1) = 1

What is the limit as x approaches 0 of (8x)/(cot(x)) ?
The limit as x approaches 0 of (8x)/(cot(x)) is 0