What is the limit as x approaches 0 of x/(2sin(6x)) ?

The limit as x approaches 0 of x/(2sin(6x)) is 1/12

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limit as x approaches 0 of x/(2sin(6x))

x \to 0 lim (\frac{x}{2 sin ( 6 x )})

\frac{1}{12}

Decimal Notation

0.08333 \dots

Solution steps

x \to 0 lim (\frac{x}{2 sin ( 6 x )})

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

= \frac{1}{2} \cdot x \to 0 lim (\frac{x}{sin ( 6 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{cos ( 6 x ) \cdot 6})

= \frac{1}{2} \cdot x \to 0 lim (\frac{1}{cos ( 6 x ) \cdot 6})

Plug in the value

x = 0

= \frac{1}{2} \cdot \frac{1}{cos ( 6 \cdot 0 ) \cdot 6}

Simplify

\frac{1}{2} \cdot \frac{1}{cos ( 6 \cdot 0 ) \cdot 6} : \frac{1}{12}

= \frac{1}{12}

x \to 2 lim (\frac{x - 2}{∣ 2 - x ∣})

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

x \to 2 lim (15)

x \to 0 lim (\frac{e ^{x}}{x ^{4}})

x \to 0 lim (ln ((x + 1)^{x}))

What is the limit as x approaches 0 of x/(2sin(6x)) ?
The limit as x approaches 0 of x/(2sin(6x)) is 1/12