What is the limit as x approaches 0-of x/(sin(3x)) ?

The limit as x approaches 0-of x/(sin(3x)) is 1/3

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limit as x approaches 0-of x/(sin(3x))

x \to 0 - lim (\frac{x}{sin ( 3 x )})

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

x \to 0 - lim (\frac{x}{sin ( 3 x )})

Apply L'Hopital's Rule

= x \to 0 - lim (\frac{1}{cos ( 3 x ) \cdot 3})

Plug in the value

x = 0

= \frac{1}{cos ( 3 \cdot 0 ) \cdot 3}

cos (3 \cdot 0) \cdot 3 = 3

= \frac{1}{3}

What is the limit as x approaches 0-of x/(sin(3x)) ?
The limit as x approaches 0-of x/(sin(3x)) is 1/3