What is the limit as x approaches 0 of 8xcot(3x) ?

The limit as x approaches 0 of 8xcot(3x) is 8/3

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limit as x approaches 0 of 8xcot(3x)

x \to 0 lim (8 x cot (3 x))

\frac{8}{3}

Decimal Notation

2.66666 \dots

Solution steps

x \to 0 lim (8 x cot (3 x))

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

= 8 \cdot x \to 0 lim (x cot (3 x))

Rewrite for L'Hopital

= 8 \cdot x \to 0 lim (\frac{x}{\frac{1}{c o t ( 3 x )}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{sec ^{2} ( 3 x ) \cdot 3})

= 8 \cdot x \to 0 lim (\frac{1}{sec ^{2} ( 3 x ) \cdot 3})

Plug in the value

x = 0

= 8 \cdot \frac{1}{sec ^{2} ( 3 \cdot 0 ) \cdot 3}

Simplify

8 \cdot \frac{1}{sec ^{2} ( 3 \cdot 0 ) \cdot 3} : \frac{8}{3}

= \frac{8}{3}

n = 1 \sum \infty (\frac{n + 1}{n})^{n}

y^{^{''}} - 2 y^{^{'}} + y = x e^{- x}

\frac{\partial}{\partial z} (x^{a} y^{b} z^{c})

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

y^{^{'}} + \frac{y}{x} = 7 x^{3} y^{2}

What is the limit as x approaches 0 of 8xcot(3x) ?
The limit as x approaches 0 of 8xcot(3x) is 8/3