What is the limit as x approaches 0 of x/(sin(12x)) ?

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

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limit as x approaches 0 of x/(sin(12x))

x \to 0 lim (\frac{x}{sin ( 12 x )})

\frac{1}{12}

Decimal Notation

0.08333 \dots

Solution steps

x \to 0 lim (\frac{x}{sin ( 12 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{cos ( 12 x ) \cdot 12})

= x \to 0 lim (\frac{1}{cos ( 12 x ) \cdot 12})

Plug in the value

x = 0

= \frac{1}{cos ( 12 \cdot 0 ) \cdot 12}

cos (12 \cdot 0) \cdot 12 = 12

= \frac{1}{12}

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