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

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

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

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

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

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})

Plug in the value

x = 0

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

cos (6 \cdot 0) \cdot 6 = 6

= \frac{1}{6}

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